The positive square root of 83−65 is

83−65=3(8−215)=34.8−215=34.(5−3)

The positive square root of 83−65 is

83−65=3(8−215)=34.8−215=34.(5−3)

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The positive square root of $8 \sqrt{3} - 6 \sqrt{5}$ is

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$\sqrt[3]{3} (\sqrt{5} - \sqrt{3})$

$\sqrt{5} - \sqrt{3}$

$\sqrt{3} (\sqrt{5} - \sqrt{3})$

$\sqrt[4]{3} (\sqrt{5} - \sqrt{3})$

answer is D.

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Detailed Solution

$\sqrt{8 \sqrt{3} - 6 \sqrt{5}}$

$= \sqrt{\sqrt{3} (8 - 2 \sqrt{15})}$

$= \sqrt[4]{3} . \sqrt{8 - 2 \sqrt{15}}$

$= \sqrt[4]{3} . (\sqrt{5} - \sqrt{3})$

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The positive square root of 83−65 is

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The positive square root of $8 \sqrt{3} - 6 \sqrt{5}$ is