SOLUTION: Does this look correct? Have I completed all steps? If not can you show me what I am missing. Your help will be much appreciated. Note the "x" is for multiplication. √175y

Algebra ->  Radicals -> SOLUTION: Does this look correct? Have I completed all steps? If not can you show me what I am missing. Your help will be much appreciated. Note the "x" is for multiplication. √175y      Log On


   

Question 374416: Does this look correct? Have I completed all steps? If not can you show me what I am missing. Your help will be much appreciated. Note the "x" is for multiplication.
√175y^6
= √175×y^2
= √175×y^2
= √175×y
Answer by jsmallt9(3759) About Me  (Show Source):
You can put this solution on YOUR website!
sqrt%28175y%5E6+%29
= sqrt%28175%2Ay%5E2+%29
Where did the 6 go??

To simplify a square root (where there are no fractions), like this one, you look for perfect square factors of the radicand. (The expression inside a radical is called the radicand.) Your radicand has a couple of perfect square factors:
sqrt%2825%2A7%2A%28y%5E3%29%5E2%29
Next I like to use the Commutative Property to rearrange the factors so the perfect squares are in front:
sqrt%2825%2A%28y%5E3%29%5E2%2A7%29
Next we use a property of radicals, root%28a%2C+p%2Aq%29+=+root%28a%2C+p%29%2Aroot%28a%2C+q%29, to separate all the perfect square factors into their own square roots:
sqrt%2825%29%2Asqrt%28%28y%5E3%29%5E2%29%2Asqrt%287%29
The square roots of the perfect squares can be simplified:
5%2Ay%5E3%2Asqrt%287%29
One more detail...
Square roots, including sqrt%28175y%5E6+%29, are supposed to be positive (or zero). Our simplified expression should also be positive (or zero), too. However,
5%2Ay%5E3%2Asqrt%287%29
could be negative if y is negative. Since we do not know that y cannot be negative, then we must use absolute value to ensure a positive (or zero) expression:
5%2Aabs%28y%5E3%29%2Asqrt%287%29
Since y%5E2 cannot be negative this can also be written as
5%2Ay%5E2%2Aabs%28y%29%2Asqrt%287%29
Either of these last two is your simplified expression.