Questions on Algebra: Radicals -- complicated equations involving roots answered by real tutors!

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is the same as in other words you simply bring the term up to the numerator and multiply it by
:

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[SQRT(x + 7)] - 2[SQRT(x)] =-2
I know x = 9
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The simplest way is to get one radical by itself, then square both sides.
[SQRT(x + 7)] - 2[SQRT(x)] =-2

Now square

Now isolate the other radical

Square again

Solved by pluggable solver: SOLVE quadratic equation (work shown, graph etc)

Quadratic equation (in our case ) has the following solutons: For these solutions to exist, the discriminant should not be a negative number. First, we need to compute the discriminant : . Discriminant d=6400 is greater than zero. That means that there are two solutions: . Quadratic expression can be factored: Again, the answer is: 9, 0.111111111111111. Here's your graph:

The onsite solver doesn't do factors correctly if the coefficient of the the x^2 is not 1, but the answers are right, 9 and 1/9.
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How tall is a stack of cube-shaped blocks whose volumes are 375 cubic inches, 648 cubic inches and 1,029 cubic inches?
A. 10 cubert(3)
B. 6 cubert(3)
C. 3 sqrt(3)
D. 4 sqrt(3)
E. 9 sqt(3)
F. 18 cubert(3)
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I don't know what you mean by that. More info is needed.

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sqrt(75)-sqrt(3)
sqrt(25*3)-sqrt3()
5sqrt(3)-sqrt(3)
(5-1)sqrt(3)
4sqrt(3) ans.

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√9/16(fraction) ----->
, ANSWER
Thank you,
Jojo

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Start with the given expression


Rewrite as .


Rewrite as .


Rewrite as .


Rewrite as .


Break up the square root.


Take the square root of the squares to eliminate the squares. In other words,


So where every variable is positive

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Start with the given expression


Multiply both numerator and denominator by the conjugate of the denominator


Combine the fractions.



FOIL (hint: use the difference of squares)


Square each value


Combine like terms.


Simplify


Distribute


So

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10.71014209

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Not clear whether you mean:

Or

.
I'll assume the later...
.

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Start with the given expression.


Now let's FOIL the expression.


Remember, when you FOIL an expression, you follow this procedure:


Multiply the First terms:.


Multiply the Outer terms:.


Multiply the Inner terms:.


Multiply the Last terms:.


---------------------------------------------------


Now collect every term to make a single expression.


Now combine like terms.


So FOILs to .


In other words, .

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Start with the given expression


Simplify to get . Note: If you need help with simplifying square roots, check out this solver.


Simplify to get .


Simplify to get .


Multiply 4 and 5 to get 20.


Since we have the common term , we can combine like terms


Combine like terms. Remember,


Now simplify to get


So simplifies to .


In other words,

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square root of 5x+11= x+3
5x+11= (x+3)^2 = x^2 + 9 +6x
5x+11 = x^2 + 6x+ 9
x^2 + x - 2 = 0
x = 1 or x=-2
(solve the quadratic equation and use the formula
x = (-b+-sqrt(b^2-4ac))/2a

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We have this: sqrt{x + 2} - 2 = x
We want to isolate the square root.
So, add 2 to both sides.
We now have this:
sqrt{x + 2} = x + 2
To remove the square root symbol, square both sides.
Doing so, we get this:
x + 2 = x^2 + 4x + 4
x^2 + 4x - x + 4 - 2 = 0
x^2 + 3x + 2 = 0
Factor this quadratic equation.
(x + 1) (x + 2) = 0
Set each factor to zero and solve for x.
x + 1 = 0
x = -1
=========================
x + 2 = 0
x = -2
==========================
To know for sure that we found the right answers, you must check.
Go back to your original question and replace x with -1 and simplify and then with -2 and simplify again. We want to get the same answer on both sides.
You were given:
sqrt{x + 2} - 2 = x
Let x = -1
sqrt{-1 + 2} - 2 = -1
sqrt{1} - 2 = -1
1 - 2 = -1
-1 = -1...IT CHECKS!!!
So, we know that x = -1.
How about x = -2? Is that true?
Let's check again.
Let x = -2.
sqrt{-2 + 2} - 2 = -2
sqrt{0} - 2 = -2
0 - 2 = -2
-2 = -2...IT ALSO CHECKS!!!
We now know that x = -2 is also a value for x.
Final answer: x = -1 and x = -2

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but k=-3 is not a solution because is <0
then the equation has no solution

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Your answer is off by a power of 10.
.
.
.
Then take the square root.

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= x + 5
Square both sides:
9x + 81 = (x + 5)^2
:
FOIL the right side
9x + 81 = x^2 + 10x + 25
:
0 = x^2 + 10x - 9x + 25 - 81
:
A quadratic equation:
x^2 + x - 56 = 0
Factors to:
(x+8)(x-7) = 0
Two solutions
x = -8
and
x = 7
:
Both solutions have to be checked in the original equation:
x= -8
= -8 + 5
= -8 + 5
= -3
3 does not = -3; x = -8 is not a solution
:
x=+7
= 7 + 5
= 12
= 12
12 = 12; x=7 is good solution

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Start with the given equation


Square both sides to get rid of the square root.


FOIL


Subtract 9x from both sides. Subtract 81 from both sides.


Combine like terms.


Notice we have a quadratic equation in the form of where , , and


Let's use the quadratic formula to solve for x


Start with the quadratic formula


Plug in , , and


Square to get .


Multiply to get


Rewrite as


Add to to get


Multiply and to get .


Take the square root of to get .


or Break up the expression.


or Combine like terms.


or Simplify.


So the possible answers are or


However, if you plug in , then the equation won't be true.


=============================================

Answer:


So the only solution is

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(3 + sqrt32)-(4 - sqrt18)
3+sqrt(16*2)-4+sqrt(9*2)
3+4sqrt2-4+3sqrt2
-1+7sqrt2 answer.

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example: 3 times the square root of 5 divided by the square root of 9
.

.
To get rid of the radical on the bottom multiply by:

to get:
.

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the 3 in the numerator (top number) reduces with the 3 in the denominator and you are left with or simply
.
.
.
If the problem reads then you will get a different answer.
in this case you will rewrite the fraction as the sqrt of the numerator over the sqrt of the denominator. So it would look like this:
.
now you have 3 to the 1st power on the top and 3 to the 1/2 power on the bottom. These reduce to 3 to the 1/2 power on top and 3 to the 0 power(which is 1) on the bottom. now you can rewrite 3 to the 1/2 power as a sqrt. The formula now looks like this:
you can multiply these to get . Since you can not pull any factors out then you should combine the terms and get:
.
look at both examples to make sure you see the differences. Then pick the example that matches your problem.
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I hope this helps!
.
Private tutoring is available. Click on my name to go to my website or email me at justin.sheppard.tech@hotmail.com for more information. If you have any other questions you can direct them to me personally and I will answer them for you.

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3 √13/3
Simplify- 3 ( square root of 13 over 3)

=
=
=
=

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the hypotenuse of a right triangle is 2.5 units long. The longer leg is 1.3 units longer then the shorter leg. Find the lengths of the sides.
:
Remember our old friend; a^2 + b^2 = c^2
:
Let x = the shorter leg
then
(x+1.3) = the longer leg:
:
Replace a & b with these expressions, replace c with 2.5
:
x^2 + (x+1.3)^2 = 2.5^2
:
x^2 + (x^2 + 2.6x + 1.69) = 6.25
:
x^2 + x^2 + 3.6x + 1.69 - 6.25 = 0; arrange to form a quadratic equation
:
2x^2 + 3.6x - 4.56 = 0
:
Using the quadratic equation, a=2; b=3.6; c=-4.56
x ~ .9938 ~ 1; the shorter leg
and
1 + 1.3 = 2.3; the longer leg
:
Check solution with calc; enter = 2.508 ~ 2.5

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Find the dimensions of a rectangle (a) with the greatest area whose perimeter is 30 feet.
Area = Length * Width
Perimeter = 2L + 2W = 30
------------------
L+W = 15
W = 15-L
Area = L*W = L*(15-L)
A = 15L - L^2
To find the maximum, set the 1st derivative to zero
15 - 2L = 0
L = 7.5
W = 7.5
The max area for a rectangle is a square, always. The max area for a given perimeter is a circle.

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I know I have to rationalize the denominator, im just not sure how it works with a square root and real number. Help, please! Thanks, Elizabeth.
11
-------
√7 + 8
//////////////////
Use the "conjugate" to get rid of radicals in the DEN. Multiply NUM and DEN by
[11*(sqrt(7) -8]/(7 - 64)
= -
Multiplying by the "conjugate" is something you'll see more of to deal with radicals and imaginaries.
and
3
--------
2√5 - √7
----------------
Same approach, multiply by
=
=

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the square root of 4e^3g x the square root of 6eg^2
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Multiply the coefficients: 4*6 = 24
Add the exponents of e: 3g + g^2 = g^2 + 3g
That's

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Start with the given expression


Distribute the negative


Group like terms.


Combine like terms.


Multiply


Simplify


So

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[(squareroot of 3) + (square root of 5)]^2
3+2sqrt(15)+5
8+2sqrt(15)
2[4+sqrt(15)]

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7 sqrt12 + 10 sqrt48
7sqrt(4*3)+10sqrt(16*3)
7*2sqrt(3)+10*4sqrt(3)
14sqrt(3)+40sqrt(3)
(14+40)sqrt(3)
54sqrt3 answer.

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how would you go about solving this problem?
7 sqrt12 + 10 sqrt48
;
Not exactly solving, You can simplify it, by factoring etc.
:
7* + 10*
:
factor inside the radicals to reveal the perfect squares\
7* + 10*
:
Extract those perfect squares
7*2* + 10*4
which is
14* + 40*
:
Now we have like terms so just add em up
54*

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2sqrt(x-5)*3sqrt(x+1)
=6*sqrt(x-5)*sqrt(x+1)
.
Ed

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Start with the given equation


Cube both sides to eliminate the cube root.


Cube 5 to get 125


Subtract from both sides.


Combine like terms on the right side.


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Answer:

So the answer is

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3 {sqrt 3}/ {sqrt 6}
Factor the number inside the radical:
3 {sqrt 3}/ {sqrt 2*3}
ReWriting it as:
3 {sqrt 3}/[{sqrt 2}{sqrt 3}]
Canceling like-terms:
3/{sqrt 2}
Multiplying numerator and denominator by {sqrt 2}:
3{sqrt 2}/2
Rewriting:
(3/2){sqrt 2}

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2 {sqrt x^3} + 5x{sqrt x} - 3{sqrt x^5}
You can rewrite as:
2 {sqrt x*x*x} + 5x{sqrt x} - 3{sqrt x*x*x*x*x}
Now, you can "pull out" pairs:
2x {sqrt x} + 5x{sqrt x} - 3x^2{sqrt x}
Factor out the sqrt x:
{sqrt x}[2x + 5x - 3x^2]
Combine like-terms:
{sqrt x}[7x - 3x^2]
Pull out the 'x':
x{sqrt x}[7-3x]

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= =
= =

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The index of a square root is 2, so we write:



Divide the index into each exponent.

Divide index 2 into the first exponent 99
  
  49
2)99
  98
   1 

49 is the quotient, so we will have  on
the outside in front of the radical.

1 is the remainder, so we will have  left
under the radical.  So far we have this:



 ---

Divide index 2 into the second exponent 87
  
  43
2)87
  86
   1 

43 is the quotient, so we will have  on
the outside in front of the radical.

1 is the remainder, so we will have  left
under the radical.  So far we have this:



 ---

Divide index 2 into the third exponent 64
  
  32
2)64
  64
   0 

32 is the quotient, so we will have  on
the outside in front of the radical.

0 is the remainder, so we will have no y's left
under the radical.  So we have:



But of course when the root is a square root,
we do not write the index, so we will drop the
index 2, and the 1 exponents as well:



Edwin

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sqrt(5^99x^87y^64) )
----------------------------------
= [sqrt(5^98*x^86*y^64)]
= 5^49*x^43*y^32*sqrt(5x)
=================================
Cheers,
Stan H.

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You wrote the question wrong.

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I'm assuming that you mean ??? Be careful to place your parenthesis in the right spot.


Start with the given equation.


Add 5 to both sides.


Add.


Square both sides to eliminate the square root.


Square 6 to get 36.


Add to both sides.


Combine like terms on the right side.


----------------------------------------------------------------------

Answer:

So the answer is

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sqrt(a-1 -5 = 1)
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That makes no sense.

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Start with the given equation


Square both sides to eliminate the square root.


FOIL the right side.


Get everything to the right side.


Combine like terms


Notice we have a quadratic equation in the form of where , , and


Let's use the quadratic formula to solve for x


Start with the quadratic formula


Plug in , , and


Negate to get .


Square to get .


Multiply to get


Rewrite as


Add to to get


Multiply and to get .


Take the square root of to get .


or Break up the expression.


or Combine like terms.


or Simplify.


So the possible answers are or


However, if you plug in back into the original equation, you'll find that the solution does not work. So this means that is NOT a solution.


===========================================

Answer:


So the solution is

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(sqrt[3] + 4sqrt[5])(2sqrt[3] – sqrt[5])
Applying FOIL:
sqrt[3]2sqrt[3] - sqrt[3]sqrt[5] + 4sqrt[5]2sqrt[3] - 4sqrt[5]sqrt[5]
2(3) - sqrt[15] + 8sqrt[15] - 4(5)
6 - sqrt[15] + 8sqrt[15] - 20
6 + 7sqrt[15] - 20
7sqrt[15] - 14
OR, you could factor:
7(sqrt[15]-2)
.
Divide:
[(x2 – 3x + 2)/(8x - 8)] ÷ [(x2 – 4)/(5x + 10)]
Focusing on the first term in the [], we can factor:
[(x-2)(x-1)/8(x-1)] ÷ [(x2 – 4)/(5x + 10)]
Canceling like-terms:
[(x-2)/8] ÷ [(x2 – 4)/(5x + 10)]
.
Now, focus on the second term in the [], we can factor:
[(x-2)/8] ÷ [(x–2)(x+2)/5(x+2)]
Canceling like-terms:
[(x-2)/8] ÷ [(x–2)/5]
.
Now, we can change the divide to multiplication by flipping one of the terms:
[(x-2)/8] * [5/(x–2)]
Canceling like-terms:
[1/8] * [5/1]
Resulting in:
5/8

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Factor numbers inside radical to it's prime numbers:

Pull out "pairs" of like numbers:


Factor out sqrt(2):

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T^2+T-20=0
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Always try to factor first. Failing that, then use the quadratic equation.
.
(T+5)(T-4) = 0
T = {-5, 4}

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Email me the problem or send me a number to contact you and I will help you.
.
justin.sheppard.tech@hotmail.com