Simplifying Some Radicals

Algebra Level 2

Simplify: $\sqrt{22 + 12\sqrt{2}}$

2\sqrt{2}

3 + 3\sqrt{2}

2 + 2\sqrt{2}

3 + 2\sqrt{2}

3\sqrt{2}

2 + 3\sqrt{2}

2 solutions

Tapas Mazumdar
Sep 28, 2016

$\begin{aligned} \sqrt{22+12\sqrt2} & = \sqrt{2 \left(11+6\sqrt 2 \right)} \\ & = \sqrt{2 {\left(3+\sqrt 2 \right)}^{2}} \\ & = \sqrt2 \left(3+\sqrt2\right) \\ & = \boxed{2+3\sqrt2} \end{aligned}$

Aadesh Shetty
Oct 25, 2015

Let, (a+b√2)^2 = 22+12√2 a^2 +2b^2+2√2ab = 22+12√2 Comparing both sides, a^2 + 2b^2 = 22 ab = 6 From above 2 equations we get, a=2, b=3 Therefore, √(22+12√2) = 2+3√2

Simplifying Some Radicals

2 solutions

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