Question

Evaluate: (√5 - √2)² + (√8 - √5)²

Answer 1

[(√5)²+(√2)²-2×√5×√2]+[(√8)²+(√5)²-2×√8×√5]
[5+2-2×√10]+[8+5-2×√40]
7-2√10+(13-4√10)
-2√10(7+11)
-2×18√10
-32√10

Answer 2

The answer is $20-6\sqrt{10}$

Solution

(√5 - √2)² + (√8 - √5)²

By using formula ,

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

$=(\sqrt{5} -\sqrt{2} )^{2} +(2\sqrt{2} -\sqrt{5} )^{2} \\=(\sqrt{5} )^{2} +(\sqrt{2} )^{2}-2*\sqrt{5} *\sqrt{2}+(\sq2\sqrt{2} )^{2} +(\sqrt{5} )^{2} -2*2\sqrt{2}*\sqrt{5} \\=5+2-2\sqrt{10} +8+5-4\sqrt{10} \\=7-2\sqrt{10}+13-4\sqrt{10}\\ =(7+13)-6\sqrt{10}\\ =20-6\sqrt{10}$

Therefore, $20-6\sqrt{10}$.

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