##### Use the quotient rule and the product rule to simplify the radical

label Algebra
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square root 175/9

Jul 24th, 2015

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According to the quotient rule for radicals, if $\sqrt[n]{a}$ and $\sqrt[n]{b}$ are real numbers

and b $\neq$ 0 and n is a natural number, then

$\sqrt[n]{\frac{a}{b}}=\frac{\sqrt[n]{a}}{\sqrt[n]{b}}$

Prime factorization of 175 is

175 = 5 x 5 x 7 = 25 x 7

Applying the quotient rule for radicals , we get

$\\ \sqrt{\frac{175}{9}}=\frac{\sqrt{175}}{\sqrt{9}}\\ \\ \sqrt{\frac{175}{9}}=\frac{\sqrt{25\times7}}{3}\\ \\ Applying\hspace{5} the\hspace{5} product\hspace{5} rule\hspace{5} for\hspace{5} radicals\hspace{5}on\hspace{5}the\hspace{5}numerator\\ \\ \sqrt{\frac{175}{9}}=\frac{\sqrt{25}\times\sqrt{7}}{3}\\ \\ \sqrt{\frac{175}{9}}=\frac{5\sqrt{7}}{3}\\$

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Jul 24th, 2015

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Jul 24th, 2015
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Jul 24th, 2015
Sep 26th, 2017
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