What is the square root of (64-x^2)?

Sep 30, 2015

$\sqrt{64 - {x}^{2}} = \sqrt{\left(8 + x\right) \left(8 - x\right)}$

$\sqrt{64 {x}^{2}} = 8 x$

Explanation:

Applying the rule for difference of 2 squares, we may write this as

$\sqrt{64 - {x}^{2}} = \sqrt{\left(8 + x\right) \left(8 - x\right)}$

If the original question had to be $\sqrt{64 {x}^{2}}$ then by laws of surds this would be equal to $\sqrt{64} \cdot \sqrt{{x}^{2}} = 8 x$