Question 122922


*[Tex \LARGE sqrt{175x^{4}}] Start with the given expression



*[Tex \LARGE \left(175x^{4}\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((175)^1x^4\right)^{\frac{1}{2}}] Rewrite 175 as {{{175^1}}}



*[Tex \LARGE (175)^{1\left(\frac{1}{2}\right)}x^{4\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 (175)^{\frac{1}{2}}x^{\frac{4}{2}}] Now multiply the exponents

 

*[Tex \LARGE (175)^{\frac{1}{2}}x^{2}] Reduce

 

*[Tex \LARGE \sqrt{175}x^{2}] Now convert back to radical notation




*[Tex \LARGE 5\sqrt{7}x^{2}] Simplify {{{sqrt(175)}}} to get {{{5*sqrt(7)}}}. Note: If you need help with simplifying square roots, check out this <a href=http://www.algebra.com/algebra/homework/Radicals/simplifying-square-roots.solver> solver</a>.




Answer:


So *[Tex \LARGE sqrt{175x^{4}}] simplifies to *[Tex \LARGE 5\sqrt{7}x^{2}]



In other words,  *[Tex \LARGE sqrt{175x^{4}}=5\sqrt{7}x^{2}]