125^1/2 + 125^1/2 - 845^1/2

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Solution

$\sqrt[2]{125} + \sqrt[2]{125} - \sqrt[2]{845} = \sqrt[2]{5 \times 5 \times 5} + \sqrt[2]{5 \times 5 \times 5} - \sqrt[2]{5 \times 13 \times 13} = 5 \sqrt{5} + 5 \sqrt{5} - 13 \sqrt{5} = 10 \sqrt{5} - 13 \sqrt{5} = \sqrt{5} (10 - 13) = \sqrt{5} \times - 3 = - 3 \sqrt{5}$

Hence, proved.

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