Question

2root 3_root2/2root3+root2

Answer 1

Simplify

Step-by-step explanation:

In the given question there is some typing mistake, so the correct question to this question as follows:

Question:

$\frac{2\sqrt{3}-\sqrt{2}}{2\sqrt{3}+\sqrt{2}}$

Multiply by conjugate:

$\frac{2\sqrt{3}-\sqrt{2}}{2\sqrt{3}+\sqrt{2}}\ \times \frac{2\sqrt{3}-\sqrt{2}}{2\sqrt{3}-\sqrt{2}}$

$\frac{(2\sqrt{3}-\sqrt{2})^2}{(2\sqrt{3})^2-(\sqrt{2})^2}$

Formula:

$(a)^2-(b)^2 =(a+b) (a-b)$

$(a+b)^2=(a)^2+(b)^2+2 \cdot a\cdot b$

$\frac{(2\sqrt{3})^2+(\sqrt{2})^2-2 \cdot (2\sqrt{3}) \cdot (\sqrt{2})}{(12-2)}$

$\frac{(12+2-4\sqrt{3}\sqrt{2})}{12-2}$

$\frac{(14-4\sqrt{6})}{10}$

$\frac{2(7-2\sqrt{6})}{10}$

$\frac{(7-2\sqrt{6})}{5}$

Learn more:

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