Question

$\frac{ \sqrt{3} }{ \sqrt{7} }$
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Answer 1

Answer:

$\sf{ {\dfrac{ {\sqrt{21}} }{ 7}} }$

Step-by-step explanation:

Given : $\sf{ {\dfrac{ {\sqrt{3}} }{ {\sqrt{7}} }} }$

Rationalising the denominator, we get

$\succ \sf{ {\dfrac{ {\sqrt{3}} }{ {\sqrt{7}} }} \times {\dfrac{ {\sqrt{7}} }{ {\sqrt{7}} }}}$

$\succ \sf{ {\dfrac{ {\sqrt{3}} \times {\sqrt{7}} }{ {\sqrt{7}} \times {\sqrt{7}} }} }$

$\succ \sf{ {\dfrac{ {\sqrt{3 \times 7}} }{ ({\sqrt{7}} )^2 }} }$

When we remove the square root over a number, the number has a power of ½.

$\succ \sf{ {\dfrac{ {\sqrt{3 \times 7}} }{ (7^2)^{\frac{1}{2}} }} }$

Identity : $\sf{(a^m)^n = a^{mn}}$

$\succ \sf{ {\dfrac{ {\sqrt{3 \times 7}} }{ 7^{2 \times {\frac{1}{2}} }}} }$

$\succ \sf{ {\dfrac{ {\sqrt{3 \times 7}} }{ 7^{{\cancel{2}} \times {\frac{1}{{\cancel{2}}}} }}} }$

$\succ \sf{ {\dfrac{ {\sqrt{21}} }{ 7}}}$

Answer 2

Step-by-step explanation:

$\frac{ \sqrt{3} }{ \sqrt{7} }$

we can multiply the this fraction with

$\sqrt{7}$

we get

$\frac{ \sqrt{3} }{ \sqrt{7} } \times \frac{ \sqrt{7} }{ \sqrt{7} }$

we get

$\frac{ \sqrt{3} \sqrt{7} }{ \sqrt{7} \times \sqrt{7} }$

we get

$\frac{ \sqrt{21} }{7}$