Question

Find fourth root of 124 – 32√15​

Answer 1

Answer:

So the value of fourth root 124+32√15 is (√3 + √5)

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Answer 2

Answer:

√5 – √3

Step-by-step explanation:

124 – 32√15

= 60 + 64 – 32√15

$(8) {}^{2} + (2 \sqrt{15} ) {}^{2} - 2.8.2 \sqrt{15}$

$= (8 - 2 \sqrt{5} ) {}^{2}$

Therefore fourth root

$= \sqrt[4]{(8 - 2 \sqrt{15} } ) {}^{2} \\ \\ = \sqrt[2]{8 - 2 \sqrt{15} } \\ \\ = \sqrt[2]{3 + 5 - 2 \sqrt{15} } \\ \\ = \sqrt[2]{3 + 5 - 2 \sqrt{15} } \\ \\ = \sqrt[2]{3 + 5 - 2 \sqrt{15} } \\ \\ = \sqrt[2]{( \sqrt{5} - \sqrt{3} }) {}^{2} \\ \\ = \sqrt{5} - \sqrt{3}$

Hence, four root of 124 – 32√15 is √5 – √3.