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

 Oct 6, 2022
 #1
avatar+1005 
+3

\(\sqrt{28 + 16\sqrt{3}}\)

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
 #2
avatar+23 
0

thhhhx

Tuckerrrr  Oct 7, 2022

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