Question

simplify 3 root 2 minus 2 root 3 by 3 root 2 + 2 root 3 + root 12 by root 3 minus root 2​

Answer 1

Answer:

11 or -1 is the answer of this question

Step-by-step explanation:

Rationalise the denominator in both the cases and u will get the answer

Answer 2

The answer is 11 + 4√6

Given

$\frac{3\sqrt{2} - 2\sqrt{3} }{3\sqrt{2} + 2\sqrt{3} } + \frac{\sqrt{12} }{\sqrt{3} - \sqrt{2}}$

To Find

Simplified value

Solution

$\frac{3\sqrt{2} - 2\sqrt{3} }{3\sqrt{2} + 2\sqrt{3} } + \frac{\sqrt{12} }{\sqrt{3} - \sqrt{2}}$

We first need to rationalize the statement

Multiplying the fractions by 3√ - 2√3 and √3 + √2 respectively we get

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

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

Now using the formula

• (a-b)² = a² - 2ab + b²
• a² - b² = (a+b)(a-b) we get,

$= \frac{18 - 12\sqrt{6} +12 }{18 - 12 } + \frac{6 + 2\sqrt{6} }{3-2}$

Summing up we get

$= \frac{30 - 12\sqrt{6} }{6 } + 6 + 2\sqrt{6}$

$= 5 + 2\sqrt{6} + 6 + 2\sqrt{6}$

= 11 + 4√6

Therefore, the answer is 11 + 4√6

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