Question

8.5 divide radical expressions (homework) score: 2/14 answered: 2/14 question 3 simplify. $\frac{sqrt{100y^{10}}}{sqrt{6^{7}}}=$ question help: video written example

Explanation:

Step1: Use quotient - rule of radicals

The quotient - rule states that $\frac{\sqrt{a}}{\sqrt{b}}=\sqrt{\frac{a}{b}}$ for $a\geq0$ and $b > 0$. So, $\frac{\sqrt{100y^{10}}}{\sqrt{6^{7}}}=\sqrt{\frac{100y^{10}}{6^{7}}}$.

Step2: Simplify the coefficient and the variable part

First, $100 = 10^{2}$ and $6^{7}=279936$. Also, using the power - rule of exponents, for the variable part, we have $\sqrt{\frac{10^{2}y^{10}}{6^{7}}}=\frac{10y^{5}}{\sqrt{6^{7}}}$. And $6^{7}=6^{6}\times6$, so $\sqrt{6^{7}} = 6^{3}\sqrt{6}=216\sqrt{6}$.

Step3: Rationalize the denominator

Multiply the numerator and denominator by $\sqrt{6}$: $\frac{10y^{5}}{216\sqrt{6}}\times\frac{\sqrt{6}}{\sqrt{6}}=\frac{10y^{5}\sqrt{6}}{216\times6}=\frac{10y^{5}\sqrt{6}}{1296}=\frac{5y^{5}\sqrt{6}}{648}$.

Answer:

$\frac{5y^{5}\sqrt{6}}{648}$