Question

$\sqrt{10 + 4 \sqrt{6 } } - \sqrt{10 - 4 \sqrt{6} }$
encuentra el valor numérico.
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Answer 1

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$x = \sqrt{10 + 4 \sqrt{6} } - \sqrt{10 - 4 \sqrt{6} } \\ x = \sqrt{6 + 4 \sqrt{6} + 4 } - \sqrt{6 - 4 \sqrt{6} + 4} \\ x = \sqrt{ {( \sqrt{6} )}^{2} + 2( \sqrt{6)} (2) + {2}^{2} } - \sqrt{ {( \sqrt{6} )}^{2} - 2( \sqrt{6)} (2) + {2}^{2} } \\ x = \sqrt{ {( \sqrt{6} + 2)}^{2} } - \sqrt{ {( \sqrt{6} }^{} - 2) {}^{2} } \\ x = \sqrt{6} + 2 - ( \sqrt{6} - 2) \\ x = 4$