SOLUTION: A square has an area of 72 square inches. What is its side length "s"? Give answer using simplified radicals. Any feedback would be appreciated. Trying to help my daughter with A

Algebra ->  Radicals -> SOLUTION: A square has an area of 72 square inches. What is its side length "s"? Give answer using simplified radicals. Any feedback would be appreciated. Trying to help my daughter with A      Log On


   

Question 941522: A square has an area of 72 square inches. What is its side length "s"?
Give answer using simplified radicals.
Any feedback would be appreciated. Trying to help my daughter with Autism spectrum disorder.
Found 2 solutions by jim_thompson5910, josgarithmetic:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Area = (side)*(side)

A+=+s%5E2

72+=+s%5E2 Plug in the given area. Now solve for 's'

s%5E2+=+72

s+=+sqrt%2872%29 Apply the square root to both sides to get rid of the exponent of 2

s+=+sqrt%2836%2A2%29

s+=+sqrt%2836%29%2Asqrt%282%29

s+=+6%2Asqrt%282%29

So the exact simplified side length is 6%2Asqrt%282%29 inches


Answer by josgarithmetic(39617) About Me  (Show Source):
You can put this solution on YOUR website!
One square of side length 1 inch will be 1 square inch, understanding that the single unit is the
shape of a square, and we use this as a reference for understanding.

The amount of surface, 72 square inches, is NOT a square value, said better, that number is not
a square number.


You may well understand the following, but it might not be what you really want to use alone:
Your square region is some s*s area, and this is s%2As=72.
We want what is s.
s=sqrt%28s%2As%29=sqrt%2872%29
s=sqrt%282%2A2%2A3%2A2%2A3%29
s=sqrt%282%2A3%2A2%2A3%2A2%29
Each pair of factors inside the square root function makes one copy of the factor outside
the square root function.
s=2%2A3%2Asqrt%282%29
highlight%28s=6%2Asqrt%282%29%29