Question

$\sqrt{\frac{256a^4{b}^4}{625a^6{b}^2}}=$ _________.

• A. $\frac{16b}{25a^2}$
• B. $\frac{16b}{25a}$
• C. $\frac{4b}{25a}$
• D. $\frac{4b^2}{25a}$

Answer 1

The correct option is B $\frac{16b}{25a}$

$\sqrt{\frac{256a^4{b}^4}{625a^6{b}^2}}$

$=\sqrt{\frac{256\times a^4\times b^4}{625\times a^6\times b^2}}$

$=\sqrt{\frac{16\times 16\times a\times a\times a\times a\times b\times b\times b\times b}{25\times 25\times a\times a\times a\times a\times a\times a\times b\times b}}$

$=\sqrt{\frac{16\times 16\times b\times b}{25\times 25\times a\times a}}=\frac{16b}{25a}$