# Converting square root to perfect square

## Homework Statement

Hi,

I have a problem in my book in which they use a method of making sqrt( 36 + x^2 ) a perfect square by simply making x = 3( t - 1/t ) and then we get 9( t + 1/t )^2 by substituting back into sqrt(36 + x^2). My question is that why did the chose 3( t - 1/t ), is there a rule?

rock.freak667
Homework Helper
What were they trying to do with the expression √(36+x2) ? For example, if they were trying to integrate, you could have made a simple trig substitution instead of trying to think of some odd set of functions to string together.

no its in an equation form,

C(x) = [(9-x) + 1.25sqrt( x^2 + 36 )], where C(x) is a function.

and they're trying to solve for x, so they used the method above, and I know how to solve it, but I lost it when they used let x = 3( t - 1/t )

rock.freak667
Homework Helper
no its in an equation form,

C(x) = [(9-x) + 1.25sqrt( x^2 + 36 )], where C(x) is a function.

and they're trying to solve for x, so they used the method above, and I know how to solve it, but I lost it when they used let x = 3( t - 1/t )

x = 3( t - 1/t ) ⇒ x2 = 9( t - 1/t )2

∴√(36+x2)=√(36+9(t- 1/t)2), how does that turn into an expression like √(a+b)2?

I do not think there rule per se for using that substitution though.

Fair enough, thanks anyway.