Question 126393



*[Tex \LARGE sqrt{180x^{4}}] Start with the given expression



*[Tex \LARGE \left(180x^{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((180)^1x^4\right)^{\frac{1}{2}}] Rewrite 180 as {{{180^1}}}



*[Tex \LARGE (180)^{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 (180)^{\frac{1}{2}}x^{\frac{4}{2}}] Now multiply the exponents

 

*[Tex \LARGE (180)^{\frac{1}{2}}x^{2}] Reduce

 

*[Tex \LARGE \sqrt{180}x^{2}] Now convert back to radical notation



*[Tex \LARGE 6\sqrt{5}x^{2}] Simplify {{{sqrt(180)}}} to get {{{6*sqrt(5)}}}. 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>




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Answer:


So {{{sqrt(180x^4)}}} simplifies to {{{6x^2*sqrt(5)}}}



In other words, {{{sqrt(180x^4)=6x^2*sqrt(5)}}}