[Math] $\sqrt {5 – \sqrt {13 + \sqrt {48}}}$

algebra-precalculus

I can't figure out how to solve this, I don't really know how or where to find the solution, even the same problems just to figure out, but I didn't find anything. Please help.
$$
\sqrt {5 – \sqrt {13 + \sqrt {48}}}
$$

I was thinking just to use a calculator, but I am not sure about this.
Any advices, any links would help very much, Thanks!!!

$$
\left(\sqrt {5 – \sqrt {13 + \sqrt{48}}}\right) = {?}
$$
How can I solve this?

Best Answer

Hint to get you started: $$\sqrt{13 + \sqrt{48}} = \sqrt{(\sqrt{12})^2 + (\sqrt{1})^2 + 2\sqrt{12}\sqrt{1}}$$

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