Question 120343
*[Tex \LARGE sqrt{36r^{2}s}] Start with the given expression



*[Tex \LARGE \left(36r^{2}s\right)^{\frac{1}{2}}] Convert the expression from radical notation to exponent notation. Remember *[Tex \LARGE \sqrt{\textrm{A}}=\sqrt[2]{\textrm{A}}=\textrm{A}^{\frac{1}{2}}]



*[Tex \LARGE \left((36)^1r^2s^1\right)^{\frac{1}{2}}] Rewrite 36 as {{{36^1}}} and {{{s}}} as {{{s^1}}}



*[Tex \LARGE (36)^{1\left(\frac{1}{2}\right)}r^{2\left(\frac{1}{2}\right)}s^{1\left(\frac{1}{2}\right)}] Now distribute the exponent Now distribute the outer exponent {{{1/2}}} to each exponent in the parenthesis. Remember {{{(x^y)^z=x^(y*z)}}}

 

*[Tex \LARGE (36)^{\frac{1}{2}}r^{\frac{2}{2}}s^{\frac{1}{2}}] Now multiply the exponents

 

*[Tex \LARGE (36)^{\frac{1}{2}}r^{1}s^{\frac{1}{2}}] Reduce

 

*[Tex \LARGE \sqrt{36}r\sqrt{s}] Now convert back to radical notation



*[Tex \LARGE 6r\sqrt{s}] Take the square root of 36 to get 6




So *[Tex \LARGE sqrt{36r^{2}s}]  simplifies to *[Tex \LARGE 6r\sqrt{s}]