Question

$X=\sqrt[6]{6(\frac{91125}{216}{)}^2},thenX=$

• A. 4.5
• B. 7.5
• C. 15
• D. 3.75

Answer 1

The correct option is B

7.5

$\sqrt[6]{6(\frac{91125}{216}{)}^2}$ can be written as

$\left(\right(\frac{91125}{216}{)}^2{)}^{\frac{1}{6}}$ = $(\frac{91125}{216}{)}^{\frac{1}{3}}$

= $\sqrt[3]{3\left(\frac{91125}{216}\right)}$

Now, by factorization we have

91125 = $3\times 3\times 3\times 3\times 3\times 3\times 5\times 5\times 5$

216 = $3\times 3\times 3\times 2\times 2\times 2$

So, $\sqrt[3]{3\left(\frac{91125}{216}\right)}$ = $\sqrt[3]{3\left(\frac{3\times 3\times 3\times 3\times 3\times 3\times 5\times 5\times 5}{3\times 3\times 3\times 2\times 2\times 2}\right)}$

= $\frac{3\times 3\times 5}{3\times 2}$

= $\frac{45}{6}$

= $\frac{15}{2}=7.5$