Question

Find the value of:

$\left(i\right)\frac{\sqrt{80}}{\sqrt{405}}$ $\left(ii\right)\frac{\sqrt{441}}{\sqrt{625}}$ $\left(iii\right)\frac{\sqrt{1587}}{\sqrt{1728}}$ $\left(iv\right)\sqrt{72}\times \sqrt{338}$ $\left(v\right)\sqrt{45}\times \sqrt{20}$

Answer 1

$\left(i\right)\frac{\sqrt{80}}{\sqrt{405}}=\sqrt{\frac{80}{405}}=\sqrt{\frac{16}{81}}\text{Dividing by 5}$

$=\sqrt{\frac{16}{81}}=\frac{4}{9}$

$\left(ii\right)\frac{\sqrt{441}}{\sqrt{625}}=\sqrt{\frac{441}{625}}=\frac{21}{25}$

$\left(iii\right)\frac{\sqrt{1587}}{\sqrt{1728}}=\sqrt{\frac{1587}{1728}}=\sqrt{\frac{1587+3}{1728+3}}=\sqrt{\frac{529}{576}}$

$\sqrt{\frac{529}{576}}=\frac{23}{24}$

$\left(iv\right)\sqrt{72}\times \sqrt{338}=\sqrt{72\times 338}=\sqrt{24336}$

$=156$

$\left(v\right)\sqrt{45}\times \sqrt{20}=\sqrt{45\times 20}=\sqrt{900}=30$