SOLUTION: i am doing my algebra 2 (10th grade) class on plato, an online schooling program. which i need some major help with. i cant find it anywhere, so i figured id give this a go. please

Algebra ->  Square-cubic-other-roots -> SOLUTION: i am doing my algebra 2 (10th grade) class on plato, an online schooling program. which i need some major help with. i cant find it anywhere, so i figured id give this a go. please      Log On


   



Question 174534: i am doing my algebra 2 (10th grade) class on plato, an online schooling program. which i need some major help with. i cant find it anywhere, so i figured id give this a go. please help me solve this equation. the+square+root+of+5xy%5E7+times+the+square+root+of+10x%5E3y%5E3 thanks
Found 2 solutions by Edwin McCravy, rapaljer:
Answer by Edwin McCravy(20055) About Me  (Show Source):
You can put this solution on YOUR website!

Since square roots are never negative we must in the
end be sure that our answer cannot be negative.  But
first:

sqrt%285xy%5E7%29sqrt%2810x%5E3y%5E3%29

Multiply what's under the radicals.

sqrt%28%285xy%5E7%29%2810x%5E3y%5E3%29%29

Simplify

sqrt%2850x%5E4y%5E10%29

The largest perfect square that will divide 
into 50 is 25, so write 50 as 25%2A2

sqrt%2825%2A2x%5E4y%5E10%29

We can take out the square root of 25 as 5
in front of the radical:

5%2Asqrt%282x%5E4y%5E10%29

The index of a square root is understood
to be 2, like this:

5%2Aroot%282%2C2x%5E4y%5E10%29

And we divide the exponents of x and y by
the index 2, getting 2 and 5.  Since there
is no remainder, we will have no x's or
y's left under the radical, but only the 2.

5%2Ax%5E2y%5E5%2Asqrt%282%29

Now we have just one more thing to take
care of.  Since we know that the answer
cannot be negative, we look at the factors:
The 5 is never negative.
The x%5E2 is never negative
The sqrt%282%29 is never negative.

However the y%5E5 just might be negative,
because if y were a negative number,
then y%5E5 would also be a negative
number.  So we must put absolute value
bars around the y to keep it from causing
the expression to be negative, so the
final answer is 

+5+%2A+x%5E2+%2A+abs%28y%29%5E5%2Asqrt%282%29+

Edwin

Answer by rapaljer(4671) About Me  (Show Source):
You can put this solution on YOUR website!
Is this your problem? sqrt%285xy%5E7%29%2Asqrt%2810x%5E3y%5E3%29+???
If so, multiply the radicands (inside the square roots!) together to get
sqrt%2850x%5E4y%5E10%29+

Sort out the perfect squares by forming two square roots:
sqrt%2825x%5E4y%5E10%29%2Asqrt%282%29+

Simplify the square root that is a perfect square:
+5x%5E2%2Ay%5E5+%2Asqrt%282%29+

If you need resources and explanations that PLATO does NOT provide, then you need to see my website!! Click on my tutor name, "rapaljer" anywhere in algebra.com, and then take my first main link on my homepage which is "Basic, Intermediate, and College Algebra: One Step at a Time." Go to Basic Algebra, Chapter 5, and you will find the ENTIRE chapter on Square Roots, complete with explanations, examples, exercises, and answers in a Discovery Method format, a LOT easier to understand than PLATO, and UNLIKE PLATO, IT's ALL FREE!!!!

Send me an Email if you need more help!!!

R^2