Question

simplify (3 -√3)^2
simplify (√5 -√3) ^2

Answer 1

$\Large{\underline{\underline{\bf{Solution :}}}}$

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★ To Find :

We have to find the present age of Meena and Meena's daughter.

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★ Solution :

$\sf{1^{st} \: case}$

$\sf{(3 - 3\sqrt{3})^2} \\ \\ \bf{We \: know \: that,} \\ \\ \Large{\implies{\boxed{\boxed{\sf{(a - b)^2 = a^2 + b^2 - 2ab}}}}} \\ \\ \sf{→ (3)^2 + (\sqrt{3})^2 - 2(3)(\sqrt{3})} \\ \\ \sf{→ 9 + 3 - 6 \sqrt{3}} \\ \\ \sf{12 - 6 \sqrt{3}}$

$\rule{200}{2}$

$\sf{2^{nd} \: case}$

$\sf{(\sqrt{5} - 3\sqrt{3})^2} \\ \\ \bf{We \: know \: that,} \\ \\ \Large{\implies{\boxed{\boxed{\sf{(a - b)^2 = a^2 + b^2 - 2ab}}}}} \\ \\ \sf{→ (\sqrt{5})^2 + (\sqrt{3})^2 - 2(\sqrt{3})(\sqrt{5})} \\ \\ \sf{→ 5 + 3 - 2\sqrt{15}} \\ \\ \sf{8 - 2 \sqrt{15}}$

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