Find the value of:
(i) $ \frac{\sqrt{80}}{\sqrt{405}} $
(ii) $ \frac{\sqrt{441}}{\sqrt{625}} $
(iii) $ \frac{\sqrt{1587}}{\sqrt{1728}} $
(iv) $ \sqrt{72} \times \sqrt{338} $
(v) $ \sqrt{45} \times \sqrt{20} $

To do:

We have to find the value of the given numbers. 

Solution:

(i)  $\frac{\sqrt{80}}{\sqrt{405}}=\sqrt{\frac{80}{405}}$

$=\sqrt{\frac{16\times5}{81\times5}}$

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

$=\frac{4}{9}$

(ii) $\frac{\sqrt{441}}{\sqrt{625}}=\sqrt{\frac{441}{625}}$

$=\sqrt{\frac{21^2}{25^2}}$

$=\sqrt{(\frac{21}{25}})^2$

$=\frac{21}{25}$

(iii) $\frac{\sqrt{1587}}{\sqrt{1728}}=\sqrt{\frac{1587}{1728}}$

$=\sqrt{\frac{529 \times 3}{576 \times 3}}$

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

Square root of 529 is,

Square root of 529 is 23.

Square root of 576 is,

Square root of 576 is 24.

Therefore,

$\sqrt{\frac{441}{625}}=\frac{23}{24}$.

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

$=\sqrt{24336}$

Square root of 24336 is,

Square root of 24336 is 156.

Therefore,

$\sqrt{72} \times \sqrt{338}=156$. 

(v) $\sqrt{45} \times \sqrt{20}=\sqrt{45 \times 20}$

$=\sqrt{900}$

$=30$

Square root of 900 is 30.

Therefore,

$\sqrt{45} \times \sqrt{20}=30$. 

Tutorialspoint

Updated on: 10-Oct-2022

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