Simplify the given equation in the attached picture:\sqrt{29-\sqrt{5}}

Mathematics

1 answer:

Vilka [71]1 year ago

3 0

Answer: 2√5 - 3

Step-by-step explanation:

$Simplify the following:$\sqrt{29-12 \sqrt{5}}$$$\begin{aligned}&29-12 \sqrt{5}=9-12 \sqrt{5}+20=9-12 \sqrt{5}+4(\sqrt{5})^{2}=(2 \sqrt{5}-3)^{2}: \\&\sqrt{\left((2 \sqrt{5}-3)^{2}\right)}\end{aligned}$$Cancel exponents. $\sqrt{(2 \sqrt{5}-3)^{2}}=2 \sqrt{5}-3$ :\\Answer:$$2 \sqrt{5}-3$

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