# Step-by-step Solution

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## Step-by-step explanation

Problem to solve:

$\left(\sqrt{2}\sqrt{13+\sqrt{7}}-2\sqrt{5-\sqrt{7}}\right)\cdot\frac{1}{\sqrt{3-\sqrt{7}}}$

Learn how to solve multiplication of numbers problems step by step online.

$\left(1.4142135623730951\cdot \sqrt{13+\sqrt{7}}-2\cdot \sqrt{5-1\cdot \sqrt{7}}\right)\frac{1}{\sqrt{3-1\cdot \sqrt{7}}}$

Learn how to solve multiplication of numbers problems step by step online. Multiply (2^0.5(13+7^0.5)^0.5-2(5-7^0.5)^0.5)1/((3-7^0.5)^0.5). The square root of 2 is \frac{6}{\sqrt{18}}. Calculate the power \sqrt{7}. Multiply the fraction and term.

$3\sqrt{2}$$\,\,\left(\approx 4.242640687119286\right)$
$\left(\sqrt{2}\sqrt{13+\sqrt{7}}-2\sqrt{5-\sqrt{7}}\right)\cdot\frac{1}{\sqrt{3-\sqrt{7}}}$