Question

$\sqrt{7 - \sqrt[2]{10} }$

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Answer 1

$\color{red}\huge{\underline{\underline{GIVEN\dag}}}$

• $\sqrt{7 -2 \sqrt{10} }$

$\color{red}\huge{\underline{\underline{SOLUTION\dag}}}$

$\implies \sqrt{5 + 2 - 2 \sqrt{10} }$

$\implies \sqrt{ { (\sqrt{5} })^{2} + ( { \sqrt{2} })^{2} - 2 \sqrt{10} }$

$\implies \sqrt{( { \sqrt{5} - \sqrt{2} })^{2} }$

$\implies \sqrt{5} - \sqrt{2}$

$\implies 2.23 - 1.41$

$\therefore{ \boxed{ \color{orange} \sqrt{7 - 2 \sqrt{10} } = \sqrt{5} - \sqrt{2} = 0.82 }}$

HOPE THAT HELPS!!