Question

rationalize the denominator of 1 by root 3 + root 2 and evaluate by taking root 2 is equals to 1.414 and root 3 is equal to 1.732​

Answer 1

I think it is helpful for you

Answer 2

Answer:

After rationalisation required answer is 0.318.

Step-by-step explanation:

Given expression is $\frac{1}{ \sqrt{3} + \sqrt{2} }$

We want to rationalize the denominator.

Here denominator is (√3+√2) and numerator is 1.

We are multiplying denominator and numerator by (√3-√2)

So,

$\frac{1 \times ( \sqrt{3} - \sqrt{2} )}{( \sqrt{3} + \sqrt{2})( \sqrt{3} - \sqrt{2} )} \\ = \frac{\sqrt{3} - \sqrt{2}}{ { \sqrt{3} }^{2} - { \sqrt{2} }^{2} } \\ = \frac{\sqrt{3} - \sqrt{2}}{3 - 2} \\ = \frac{\sqrt{3} - \sqrt{2}}{1} \\ = \sqrt{3} - \sqrt{2}$

It is also given that √2 = 1.414 and √3 = 1.732

So,

$\sqrt{3} - \sqrt{2} \\ = 1.732 - 1.414 \\ = 0.318$

Here applied formula is

${x}^{2} - {y}^{2} = (x + y)(x - y)$

This is a problem of Power of indices .

Some important formulas of Power of indices:

${x}^{0} = 1 \\ {x}^{1} = x \\ {x}^{a} \times {x}^{b} = {x}^{a + b} \\ \frac{ {x}^{a} }{ {x}^{b} } = {x}^{a - b} \\ {x}^{ {y}^{a} } = {x}^{ya} \\ {x}^{ - 1} = \frac{1}{x} \\ {x}^{a} \times {y}^{a} = {(xy)}^{a}$

Power of indices related two more questions:

https://brainly.in/question/20611233

https://brainly.in/question/8929724

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