How do you simplify $\sqrt{37 - 4 \sqrt{75}}$ $sqrt(37-4sqrt(75))$ ?

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How do you simplify $\sqrt{37 - 4 \sqrt{75}}$ $sqrt(37-4sqrt(75))$ ?

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Answer 1 · 2018-01-16T22:57:31

$\sqrt{37 - 4 \sqrt{75}} = 5 - 2 \sqrt{3}$ $sqrt(37-4sqrt(75)) = 5-2sqrt(3)$

Explanation:

I think you mean the positive square root of $37 - 4 \sqrt{75}$ $37-4sqrt(75)$

Note that:

$37 - 4 \sqrt{75} = 37 - 4 \sqrt{5^{2} \cdot 3}$ $37-4sqrt(75) = 37-4sqrt(5^2*3)$

$37 - 4 \sqrt{75} = 37 - 20 \sqrt{3}$ $color(white)(37-4sqrt(75)) = 37-20sqrt(3)$

$37 - 4 \sqrt{75} = 5^{2} - 2 (5) (2 \sqrt{3}) + 3 \cdot 2^{2}$ $color(white)(37-4sqrt(75)) = 5^2-2(5)(2sqrt(3))+3*2^2$

$37 - 4 \sqrt{75} = {(5 - 2 \sqrt{3})}^{2}$ $color(white)(37-4sqrt(75)) = (5-2sqrt(3))^2$

Also note that $2 \sqrt{3} \approx 3.464 < 5$ $2sqrt(3) ~~ 3.464 < 5$ , So $5 - 2 \sqrt{3} > 0$ $5-2sqrt(3) > 0$ .

So:

$\sqrt{37 - 4 \sqrt{75}} = 5 - 2 \sqrt{3}$ $sqrt(37-4sqrt(75)) = 5-2sqrt(3)$

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How do you simplify $\sqrt{37 - 4 \sqrt{75}}$ $sqrt(37-4sqrt(75))$ ?

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How do you simplify √37−4√75sqrt(37-4sqrt(75)) ?

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How do you simplify $\sqrt{37 - 4 \sqrt{75}}$ $sqrt(37-4sqrt(75))$ ?