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# $\sqrt{53+20\sqrt{7}}$ can be written in the form $a+b\sqrt{c}$, where $a,$ $b,$ and $c$ are integers and $c$ has no factors which is a perf

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$\sqrt{53+20\sqrt{7}}$ can be written in the form , where   and  are integers and  has no factors which is a perfect square of any positive integer other than 1. Find.$abc$

Nov 18, 2020

### 2+0 Answers

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Simplify the following:
sqrt(20 sqrt(7) + 53)

53 + 20 sqrt(7) = 25 + 20 sqrt(7) + 28 = 25 + 20 sqrt(7) + 4 (sqrt(7))^2 = (2 sqrt(7) + 5)^2:
sqrt((2 sqrt(7) + 5)^2)

Cancel exponents. sqrt((5 + 2 sqrt(7))^2) = 2 sqrt(7) + 5:

5 + 2 sqrt(7)        abc =5 x 2 x 7 = 70

Nov 18, 2020
edited by Guest  Nov 18, 2020
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I meant a+b+c

Nov 18, 2020