Insert an irrational number between √5 and √7 .

consider the squares of and = 5 and = 7 As, , it follows that therefore , lie between and Hence, irrational number between and is .

Mathematics

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consider the squares of $\sqrt{5}$ and $\sqrt{7}$

${(\sqrt5)^2}$ = 5 and ${(\sqrt7)^2}$ = 7

As, $5 \lt 6\lt 7$ , it follows that

$\sqrt{5} \lt \sqrt{6} \lt \sqrt{7}$ therefore , $\sqrt{6}$ lie between $\sqrt{5}$ and $\sqrt{7}$

Hence, irrational number between $\sqrt{5}$ and $\sqrt{7}$ is $\bold{\sqrt{6}}$ .

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