Question

simplify 1 by root 3 + root 2 minus 2 by root 5 minus root 3 minus 3 by root 2 minus root 5​

Answer 1

Answer:

Step-by-step explanation:

Answer 2

Concept

We will multiply in numerator and denominator by a quantity so that the eliminate the square root from the denominator in each term. And then solve the reduced equation to get the final value. Since we also know that the formula which is as follows,

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

where a and b are any numbers.

Given

The given expression is as follows,  

$\dfrac{1}{\sqrt{3} + \sqrt{2}} - \dfrac{2}{\sqrt{5} - \sqrt{3}} - \dfrac{3}{\sqrt{2} - \sqrt{5}}$

Find

We are asked to calculate the reduced value of the given expression.

Solution

Since, $\dfrac{1}{\sqrt{3} + \sqrt{2}} - \dfrac{2}{\sqrt{5} - \sqrt{3}} - \dfrac{3}{\sqrt{2} - \sqrt{5}}$

Therefore, multiplying by corresponding term in the numerator and  denominator to reduce it, we have

$\dfrac{\sqrt{3} - \sqrt{2}}{(\sqrt{3} + \sqrt{2})(\sqrt{3} - \sqrt{2})} - \dfrac{2(\sqrt{5} + \sqrt{3})}{(\sqrt{5} - \sqrt{3})(\sqrt{5} + \sqrt{3})} - \dfrac{3(\sqrt{2} + \sqrt{5})}{(\sqrt{2} - \sqrt{5})(\sqrt{2} + \sqrt{5})}\\= \dfrac{\sqrt{3} - \sqrt{2}}{3 - 2} - \dfrac{2(\sqrt{5} + \sqrt{3})}{5 - 3} - \dfrac{3(\sqrt{2} + \sqrt{5})}{2 - 5}\\= \sqrt{3} - \sqrt{2} - ( \sqrt{5} + \sqrt{3}) + \sqrt{2} + \sqrt{5}\\= 0$

Hence the calculated value of the given expression comes out to be 0.

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