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# Help plz, I need explanation

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$$sqrt\left(28+16sqrt\left(3\right)\right)$$

Oct 6, 2022

#1
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$$\sqrt{28 + 16\sqrt{3}}$$

If you want to turn that to $$a+ b\sqrt{c}$$, here's how.

First the c is obviously a 3, because what else would it be duhhh.

$$28 + 16\sqrt{3} = (a + b\sqrt{3})^2 = a^2 + 2ab\sqrt{3} + 3b^2$$

$$2ab\sqrt{3} = 16\sqrt{3}$$

$$ab = 8$$

$$a^2 + 3b^2 = 28$$

If a and b are integers, you can guess and check a little bit. After some testing, you will find that:

$$(a, b) = (4, 2)$$

So: $$\sqrt{28+16\sqrt{3}} = 4 + 2\sqrt{3}$$

Oct 6, 2022
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thhhhx

Tuckerrrr  Oct 7, 2022