Question

Simplify (root 2 plus root 5) whole square
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Answer 1

$\color{red}\large\underline{\underline{Question:}}$

$\big(\sqrt{2} + \sqrt{5}\big)^{2}$

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$\color{purple}\large\underline{\underline{To\:Find:}}$

$\mathtt{The\:simplification\:of\:the\:Equation.}$

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$\color{blue}\large\underline{\underline{Concept:}}$

Using the identity :

$(a + b)^{2} = a^{2} + b^{2} + 2ab$

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$\color{orange}\large\underline{\underline{Solution:}}$

$\big(\sqrt{2} + \sqrt{5}\big)^{2}$

$\Rightarrow \big((\sqrt{2})^{2} + (\sqrt{5})^{2} + 2 (\sqrt{2})(\sqrt{5})\big)$

$\Rightarrow \big(2 + 5 + 2 (\sqrt{10})$

$\Rightarrow \big(7 + 2 (\sqrt{10})$