Question

What is the square root of 75 46/49​

Answer 1

$Square \:root \: of \: 75 \frac{46}{49}$

$= \sqrt{ \frac{(75 \times 49 )+46}{49} }$

$= \sqrt{ \frac{3675 + 46 }{49} }$

$= \sqrt{\frac{3721}{49}}$

$= \sqrt{ \frac{61 \times 61 }{7 \times 7 } }$

$= \sqrt{ \Big( \frac{61}{7}\Big)^{2}}$

$= \frac{61}{7}$

Therefore.,

$\red{Square \:root \: of \: 75 \frac{46}{49} }$

$\green { = \frac{61}{7}}$

$\green { = 8\frac{5}{7}}$

•••♪

Answer 2

$\dag \: { \red{ \tt{ \underline{Answer :- }}}}$

$\tt \: The \: \: square \: \: root \: \: of \: \: \red{75 \frac{46}{49} } \: is \: { \underline{ \green{ \frac{61}{7} .}}}</h3><h3>$

$\dag \: { \blue{ \tt{ \underline{Solution :- }}}}$

$\implies \: \tt \: 75\frac{46}{49}$

$\implies \: \tt \sqrt{\frac{75 \times49 + 46 }{49} }$

$\implies \: \tt \: \sqrt{ \frac{3675 + 46}{49} }$

$\implies \: \ \tt \: \sqrt{ \frac{3721 }{49} }$

$\implies \: \tt \sqrt{ \frac{61 \times 61}{7 \times 7} }$

$\implies \: \tt\sqrt{ (\frac{61}{7}) {}^{2} }$

$\implies \: \huge \: { \boxed{ \underline{ \pink{ \tt{ \frac{61}{7} }}}}}$