On my recent math test I got a strategic thinking or higher level problem incorrect. This is the problem:

In the diagram y=√37. Use Pythagorean Theorem to find x. Express x as a radical expression in simplest form. Show your work.

 

For the triangle the measurements are A=6, B=6.

The Pythagorean Theorem is a²+b²=c²

 So 6²+6²=c²

 36+36=c²

 72=c²

 √72=√c

 Now you have to write c or x as a radical expression. 

 Use the perfect squares square root of 9 to be expressed as

 √72=√8*√9

 Simplify

The square root of 8 is √2*√4 which could be simplified to √2*2 because the √4 is 2.  The square root of 9 is 3.

 This is written as 3*2*√2

 6√2 is the answer.