Using the identity nbsp;(a + b)2 = a2 + 2ab + b2, we get 5+22=52+252+22 #160; #160; #160; #160; #160; #160; #160; #160; #160; #160; #160 ...

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Expansion of (x^2 - y^2)

Simplify : 5+...

Question

Simplify : ${(\sqrt{5} + \sqrt{2})}^{2} .$

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Solution

Using the identity (a + b)² = a² + 2ab + b², we get
${(\sqrt{5} + \sqrt{2})}^{2} = {(\sqrt{5})}^{2} + 2 (\sqrt{5}) (\sqrt{2}) + {(\sqrt{2})}^{2} = 5 + 2 \sqrt{2 \times 5} + 2 = 7 + 2 \sqrt{10}$
Hence, ${(\sqrt{5} + \sqrt{2})}^{2} = 7 + 2 \sqrt{10}$ .

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