Question

$\sqrt{2} = 1.414 \: and \: \sqrt{7} = 2.616 \:$
then find the value of
$\sqrt{( \frac{200}{63})}$

Answer 1

$\textbf{ \huge{ Hello Mate! }}$

Given : ⤵⤵⤵

$\sqrt{2} = 1.414 \\ \\ \sqrt{7} = 2.616$

Now, lets express question another manner.

$\sqrt{( \frac{200}{63}) } = \frac{ \sqrt{200} }{ \sqrt{63} } \\ \\ \frac{ \sqrt{2 \times 100} }{ \sqrt{7 \times 9} }$

We know well that under root of 100 and 9 are 10 and 2 respectively.

$\frac{ \sqrt{2} \times 10 }{ \sqrt{7} \times 3 } \\ = \frac{1.414 \times 10}{2.616 \times 3} \\ = \frac{1414 \times 10}{2616 \times 3} = \frac{14140}{7848}$
By cancelling we get,

= 7070 / 3924 = 3535 / 1962

Have great future ahead!