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I know this may be a basic question, but I cannot seem to get the right simplification process for the following equation:

$\sqrt{36+64+5^2} + \sqrt{20}$

I do know that the correct answer is 7√5, but I cannot seem to arrive at this answer.

This is how I broke it down.

Option 1:

√105 + 2√5

Option 2:

√100 + 5 + 2√5
10 + 5 + 2√5
15 + 2√5

I appreciate feedback on where I made a mistake.

Rook
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  • $10+5+2\sqrt{5}$ is not $17\sqrt{5}$ because $15+2\sqrt{5} \neq 17\sqrt{5}$. You need $15\sqrt{5}+2\sqrt{5}$ to get $17\sqrt{5}.$ – user1390 Jun 12 '18 at 21:50
  • Did you mean $\sqrt{36 + 64 + 5^2} + \sqrt{20}$? Please read this tutorial on how to typeset mathematics on this site, then edit your question. – N. F. Taussig Jun 12 '18 at 21:51

1 Answers1

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Note that $36+64+5^2=125,$ not $105$. Then $\sqrt{125}=5\sqrt 5$ and $\sqrt{20}=2\sqrt 5$ so the sum is $7\sqrt 5$

Ross Millikan
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  • Thank you. All along I thought that the exponent of 2 gets canceled out when the number is squared. – Rook Jun 12 '18 at 22:01
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    If you have $\sqrt{(stuff)^2}$ the square root and the square cancel (but watch out for the absolute value). In this case the $5^2$ is part of stuff, the whole of stuff is not squared, so we need to evaluate stuff before we take the square root and the square does not cancel. – Ross Millikan Jun 12 '18 at 22:37
  • Yes, I realized that as well. Thank you. – Rook Jun 13 '18 at 07:32