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Tutors Answer Your Questions about Square-cubic-other-roots (FREE)
Question 283671: I need to solve using Completing the square
x squared=-4x-2
Found 2 solutions by oberobic, richwmiller:
Answer by oberobic(528)   (Show Source):
You can put this solution on YOUR website!
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Add 4x to both sides
.
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This is conceptually ax^2 + bx = c
.
To complete the square, take 1/2*b, square it, and add it as a new 'c'.
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.
.
.
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hmmmm....that means we have an imaginary number in here, since we have a squared term on the left and a negative number on the right.
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.
Answer by richwmiller(3952)  (Show Source):
Question 283662: I don't understand why 2/3 can become 2 times 1/3. Can you shed
light on this?
Found 3 solutions by Edwin McCravy, oberobic, JenniferTutors:
Answer by Edwin McCravy(3640) (Show Source):
You can put this solution on YOUR website!I don't understand why 2/3 can become 2 times 1/3. Can you shed
light on this?
Do you understand why 2 apples can become 2 times 1 apple?
Do you understand why 2 books can become 2 times 1 book?
Do you understand why 2 pizzas can become 2 times 1 pizza?
Do you understand why 2 things can become 2 times 1 thing?
Do you understand why 2 thirds can become 2 times 1 third?
If so, you now understand why 2/3 can become 2 times 1/3!
Edwin
Answer by oberobic(528) (Show Source):
Answer by JenniferTutors(69)  (Show Source):
Question 283581: ``simplify the square root of 144z^8. please and show all work.''
Answer by jim_thompson5910(14954) (Show Source):
You can put this solution on YOUR website!
 Start with the given expression.
 Factor  into 
 Break up the square root using the identity  .
 Take the square root of  to get  .
 Take the square root of  to get  .
 Multiply.
==================================================
Answer:
So simplifies to
In other words,  where  .
Question 283573: simplify the cube root of 216a^3b^9. Please and show all work. Thanks.
simplify the square root of (y+2)^2. Please and show all work. Thanks.
Answer by vleith(2109) (Show Source):
Question 283570: simplify the square root of 144z^8. please and show all work.
Answer by vleith(2109) (Show Source):
Question 283315: What is the perimeter and area of the rectangle the top side is 3+6 times the square root of 2 yards and the right side is the square root of 8 yards.
Answer by jsmallt9(1067) (Show Source):
You can put this solution on YOUR website!Let 
and 
With these variables,
perimeter = 2x + 2y
and
area = x*y
Before we start using these formulas, let's simplify y.  has a perfect square factor of 4 so it can be simplified. (  cannot be simplified further.)
Now let's use the formulas.
Perimeter = 2x + 2y = 
Area = x*y = 
Question 283317: What is the perimeter and area of the rectangle the top side is 3+6 times the square root of 2 yards and the right side is the square root of 8 yards.
Answer by mananth(585)  (Show Source):
You can put this solution on YOUR website!What is the perimeter and area of the rectangle the top side is 3+6 times the square root of 2 yards and the right side is the square root of 8 yards.
length = 3+6sqrt2
width= sqrt8
perimeter = 2(3+6sqrt2) + 2 (sqrt8)
= 6+12sqrt2+2sqrt8
=6+12sqrt2+2*2 sqrt2----------------- 2sqrt8 = 2sqrt (2*4)=2sqrt2*sqrt4 =4sqrt2
=6+12sqrt2+4sqrt2
=6+16sqrt2 yards = perimeter
Area = L*W
= (3+6sqrt2)*2sqrt8
=(3+6sqrt2)*4sqrt2
=4sqrt2 +24sqrt2
=28sqrt2 square yards is the area
Question 283063: If 
what would the values of n and a be?
Answer by nabla(459) (Show Source):
Question 283062: Hi, how would you simplify the following algebraic expression? 
Answer by richwmiller(3952) (Show Source):
Question 283064: 
I am having a lot of trouble with this question
Answer by richwmiller(3952) (Show Source):
You can put this solution on YOUR website!There is no question. That is an expression.
Do you want to ask a question about the expression?
I didn't think so.
It could be combined to form one fraction 1/(x-y)
y/(x^2-xy) + 1/x
factor
y/(x*(x-y))+1/x
y/x*(x-y)+(x-y)/(x*(x-y))
y+x-y/(x*(x-y)
x/x*(x-y)
1/(x-y)
Question 283065: how do you solve 
Answer by richwmiller(3952) (Show Source):
Question 283066:  I'm having so much trouble with this question, nothing is working for me.
Found 2 solutions by mananth, richwmiller:
Answer by mananth(585) (Show Source):
You can put this solution on YOUR website!
(x-6)/(x^2-6x+x-6) - (x+3) / x^2+6x+2x+12)
(x-6)/ {x(x-6)+1(x-6)} - (x+3) / {x(x+6)+2(x+6)}
(x-6) / (x+1)(x-6) - (x+3)/(x+6)(x+2)
1/ (x+1) - (x+3) / (x+6)(x+2)
(x+6)(x+2) - (x+1)(x+3) / (x+1)(x+6)(x+2)
(x^2+8x+12) - (x^2+4x+3) / (x+1)((x+6)(x+2)
(x^2+8x+12-x^2-4x-3)/(x+1((x+6)(x+2)
(4x-9)/(x+1)(x+6)(x+2)
Answer by richwmiller(3952) (Show Source):
You can put this solution on YOUR website!Just looking at it I would suspect that (x-6) and/or (x+3) are factors of the denominators.
Answer : 
or Answer: 
How did I get there?
Start with
The long way:
multiply first fraction by  and the second fraction by  aka  to make a common denominator
= 
multiply it out = 
collect terms = 
add = 
rearrange
Answer:
or
Answer :
Another way to to do the same thing:
The short way:
multiply by
multiply by
multiply out the numerators
and get the same as above.
Answer :
Question 283050: How do you solve  ?
Answer by mananth(585) (Show Source):
You can put this solution on YOUR website!sqrt a^2*b^3 * cube root of ab
= a*b^3/2 * (ab)^1/3
=a*a^1/3* b^3/2 * b^1/3
=a^(1+1/3) *b^(3/2+1/3)
=a^4/3 * b^11/6
=a^4/3*b^11/3
= cube root of (a^4*b^11)
Question 283051: How would you solve  ?
I thought it might invole the difference of two squares formula, but I am not sure how to apply it to this question.
Answer by jim_thompson5910(14954) (Show Source):
You can put this solution on YOUR website! Start with the given expression.
 Factor the numerator (using the difference of squares formula).
 Factor out the GCF 3 from the denominator.
 Highlight the common terms.
 Cancel out the common terms.
 Simplify.
So simplifies to
In other words, 
Question 282954: how do i factor sqrt 48a^2b
Answer by oberobic(528) (Show Source):
Question 282809: find the square root of x^2+2x+1=9
Answer by richwmiller(3952) (Show Source):
You can put this solution on YOUR website!You can't find the square root of an equation.
You can find the square roots of each side.
first we factor the left side.
(x+1)^2=9
x+1=-3
x=-4
x+1=3
x=2
x=(2,-4)
Question 282310: What is the square root of 2X^2
Answer by edjones(4080)  (Show Source):
Question 282316: solve the square root of 6x+19=x-6
Answer by subudear(23) (Show Source):
You can put this solution on YOUR website!sqrt(6x+19)=x-6
squaring both the sides
6x + 19 = (x - 6)^2
6x + 19 = x^2 - 12x + 36
x^2 - 18x + 17 = 0
x^2 - 17x - x +17 = 0
x(x - 17) - (x - 17) = 0
(x - 17)(x - 1)=0
therefore x = 17 and 1 are the solutions.
Question 282318: Solve x^2+9x=12 by completing the square
Answer by nerdybill(2712)  (Show Source):
Question 281987: what are the possible rational roots of x^3+4x^2+2x+1=o how do you do this
Answer by stanbon(29613) (Show Source):
Question 281988: find the irrational roots of the equation x^3+4x^2+2x+1=0 im not sure how to do this
Answer by stanbon(29613) (Show Source):
You can put this solution on YOUR website!find the irrational roots of the equation x^3+4x^2+2x+1=0 im not sure how to do this
First, you have to find the rational root.
-------------
I graphed it and got x = -3.51154..
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That does not help to find the irrational roots.
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Cheers,
Stan H.
Question 281739: Please help me to solve this question:
Answer by Edwin McCravy(3640) (Show Source):
Question 281500: i dont no ow to do this...
x-2√x=8
Answer by jsmallt9(1067) (Show Source):
You can put this solution on YOUR website!
In general, to solve equations where the variable is inside a square root: - Isolate a term with a square root.
- Square both sides of the equation.
- If there is still a square root, repeat steps 1 and 2 until there are no more square roots.
- At this point the equation should have no square roots. Use appropriate techniques to solve this equation.
- Check your answer(s). This is not optional. At step 2 you squared both sides of the equation. Whenever this is done, extraneous solutions may be introduced. Extraneous solutions are solutions that work in the squared equation but do not work in the original equation. So you must check your answer(s) to see if you have any extraneous solutions. Reject any extraneous solutions.
Let's see how this works on your equation.
1. Isolate a term with a square root.
You have only one such term. To isolate it (get it by itself), all we have to do is subtract x from each side:
2. Square both sides.
The left side is a single term so it is easy to square. The right side is a binomial (two-term expression) so we have to use FOIL or the pattern,  , to square it correctly:
which simplifies to:
3. Repeat steps 1 and 2 until there are no more square roots.
There are no square roots left so we can move to step 4.
4. Solve the equation.
This is a quadratic equation so we want one side to be zero. So we'll subtract 4x from each side:
Then we factor (or use the Quadratic Formula). This factors easily:
From the Zero Product Property we know that this product is zero only if one of the factors is zero. So:
16-x = 0 or 4-x = 0
Solving these we get:
x = 16 or x = 4
5. Check your solution(s).
Always use the original equation to check:
Checking x = 16:
16 -2(4) = 8
16 - 8 = 8
8 = 8 Check!
Checking x = 4:
4 -2(2) = 8
4 - 4 = 8
0 = 8 Dose not check! We must reject this solution.
A faster, clever way to solve this is to recognize that in your original equation:
you have x and  . And since  this equation is quadratic in . We can solve it directly as a quadratic equation:
Get one side zero:
Factor:
It can be difficult to see this factoring. If so, then try using a temporary variable:
Let 
then 
and the equation becomes:
The factoring should be easier to see now:
(q-4)(q+2) = 0
If we replace the q's with we have the factored equation we found earlier:
Use the Zero Product Property:
 or 
Solving:
 or 
Since square roots cannot be negative, we reject the second equation. Solving the first equation we square both sides:
x = 16
Check the solution. (We checked this above and it works.)
Question 281592: answer for simplify Quadratic equations and functions the radical expression is 9/49=
Answer by richwmiller(3952) (Show Source):
Question 281607: Find the square root of c^3
Answer by richwmiller(3952) (Show Source):
Question 280762: the base of a 15 -ft ladder is 5ft away from a wall.How far above the floor is the top of the ladder?
Answer by jsmallt9(1067) (Show Source):
You can put this solution on YOUR website!Walls are perpendicular to floors. So there is a 90 degree angle there. This means that the ladder, the floor (between the wall and the ladder) and the wall (between the floor and the ladder) form a right triangle with the ladder as the hypotenuse and the floor and the wall forming the legs.
Use the equation for the Pythagorean Theorem to solve this problem.
Question 280777: what does the expression the square root of 90 x the square root of 40 - the sqaure root of 8 x the square root of 18 simplifies to what
Answer by jsmallt9(1067) (Show Source):
You can put this solution on YOUR website!
We could multiply the square roots first but we would get large radicands to simplify. Instead we'll simplify the square roots first. Simplifying square roots involves factoring out perfect square factors:
Using the property of radicals,  , to separate the perfect square factors into their own square roots:
Now we can replace the square roots of the perfect squares:
Within the two products we can use the Commutative and Associative properties to rearrange the order and grouping:
Multiplying we get:
Subtracting we get:
48
If you had multiplied first you would get:
These cannot be subtracted because they are like terms. But you can simplify the two square roots. They end up being nice whole numbers we can be subtracted and this subtraction, if you've done everything correctly, results in 48.
Question 280781: if the square root of 84 is simplified to a x the square root of b such that a and b are integers, what is the value of a?
Answer by jsmallt9(1067) (Show Source):
You can put this solution on YOUR website!The short way to say your problem: Simplify  and then say what number ends up in front of the square root.
Simplifying square roots involves factoring out perfect square factors, if any, and rationalizing denominators. has no denominators so do not be concerned with rationalizing. All we have to do is see if 84 has any perfect square factors.
4 is a perfect square and it is a factor of 84 so:
Like reducing fractions, you keep simplifying square roots until you can go no further. 21 has no perfect square factors so we cannot simplify any further.
Since simplifies to  , the answer to the problem is: 2.
Question 280783: express in radical form, what is the product of 2 x the square root of 7 and 3 x the square root of 5
Answer by jsmallt9(1067) (Show Source):
You can put this solution on YOUR website!
Since this is all multiplication and since multiplication is Commutative and Associative we can change the order and grouping any way we choose:
For the square roots we can use the property of radicals,  to multiply them:
The only thing left is to simplify the square root, if possible, by factoring out perfect squares. But 35 has no perfect square factors so it will not simplify.
Question 281390: write each rational expression in simplified radical form? square of 2/square of 18
Found 2 solutions by Mathematicians, subudear:
Answer by Mathematicians(79)  (Show Source):
You can put this solution on YOUR website!This one is tricky but you want to remember one important property.
If you have  , this is the same thing as  .
With that general fact in mind, we can see that
Now we want to simplify the expression inside the square root. 
Since the above fact is an equivalence relation, we see the symmetric property that
so
The easiest way to take the square root of number is to break it up into prime factorizations and remember sqrt(1) = 1
9 is the same thing as 3 * 3
so 
and 
This was a long explanation of all the work in between, in general, when you do square roots, it's easy to go from one step to the next without showing every detail in between.
For example 
Answer by subudear(23) (Show Source):
Question 281278: factor aČ + 12a + 36
Found 2 solutions by josmiceli, vleith:
Answer by josmiceli(3359) (Show Source):
You can put this solution on YOUR website!I like to use completing the square
Note that this is in the form
The left side is a perfect square:
This equation has a double root which is
check:
OK
Answer by vleith(2109) (Show Source):
Question 280782: express 5 x the square root of 72 in simplest radical form?
Answer by oberobic(528) (Show Source):
Question 280696: Find the three cube roots of 125. Show all work. Express exact answers in polar point form. Thanks!
Answer by richwmiller(3952) (Show Source):
Question 280506: How many infection cases will be 16 years from now, in millions
N Squared x+4
Answer by liljimmy0707(1) (Show Source):
Question 280407: sqrt(4/81x^8)
Answer by dabanfield(606) (Show Source):
Question 280187: what is the cube root of 108? I know it comes out to some kind of imaginary number?
Answer by richwmiller(3952) (Show Source):
Question 279870: Solve .
√6x-2=4.
Answer by checkley77(9435) (Show Source):
You can put this solution on YOUR website!IF you mean:
sqrt(6x-2)=4 then:
Square both sides.
6x-2=16
6x=16+2
6x=18
x=18/6
x=3 ans.
IF you mean:
sqrt2x-2=4 then:
sqrt2x=4+2
sqrt2x=6
Square both sides.
2x=36
x=36/2
x=18 ans.
Question 279185: solve sqrty +sqrt(y+7)=7 please help thanks abunch
Answer by jsmallt9(1067) (Show Source):
You can put this solution on YOUR website!
To solve equations where the variable is inside a square root: - Isolate a square root.
- Square both sides of the equation (remembering that exponents do not distribute).
- If there is still a square root, repeat steps #1 and #2.
- Solve the equation (which should not have any square roots remaining).
- Check your answer(s)! This is not just a good idea. It is important. At step #2 we squared both sides of an equation. Squaring both sides of an equation is not wrong. But it can introduce what are called extraneous solutions. Extraneous solutions are solutions which fit the squared equation but do not fit the original (pre-squared) equation. We must check for these extraneous solutions and reject them.
Let's see how this works on your equation.
1. Isolate a square root.
I'll subtract the second square root from each side:
The square root on the left is isolated.
2. Square both sides:
The left side, since it is a single term, is simple to square. On the right side, with two terms, we must use FOIL or the pattern  :
which simplifies to:
or
3. If there is still a square root repeat steps #1 and #2. We still have s square root so...
Isolate a square root. There is only one square root so that's the one we need to isolate. Subtracting y and 56 from each side:
Divide both sides by -14:
Square both sides:
16 = y + 7
There are no more square roots so we can move to step 4.
4. Solve.
Subtract 7 from each side:
x = 9
5. Check the solution(s).
Always use the original equation to check.
Checking x = 9:
 Check!
Question 279863: How do you simplify  ?
Answer by Alan3354(8327)  (Show Source):
You can put this solution on YOUR website!How do you simplify ?
Multiply NUM and DEN by (xy)^(1/2)
= 
---
=  = x^(13/6)*y^(3/2)
= x^2y*x^(1/6)*sqrt(y)
or x^2y*6th root(xy^3)
Simplified can be a matter of opinion
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