Question

rationalize the denomenator 1/3+√7​

Answer 1

Step-by-step explanation:

Question :—

$\mathrm{Rationalize \: the \: denomenator } : \: \frac{1}{3 + \sqrt{7} }$

Solution:—

Let's solve the problem,

We have,

$\frac{1}{3 + \sqrt{7} }$

The denominator is in the form of a+√b, so we multiply the numerator and denomination by a-√b to rationalise the denominator,

So, friend rationalising factor of 3+√7 is 3-√7.

Now,

$⟹ \frac{1}{3 + \sqrt{7} } \times \frac{3 - \sqrt{7} }{3 - \sqrt{ 7 } }$

$⟹ \frac{1(3 - \sqrt{7} )}{(3 + \sqrt{7})(3 - \sqrt{7} ) }$

⬤ Applying Algebraic Identity(a+b)(a-b) = a² - b² to the denominator We get,

$⟹ \frac{3 - \sqrt{7} }{(3 {)}^{2} - ( \sqrt{7} {)}^{2} }$

$⟹ \frac{3 - \sqrt{7} }{9 - 7}$

$⟹ \frac{3 - \sqrt{7} }{2}$

Hence, the denominator is rationalised.

Answer :—

$\frac{3 - \sqrt{7} }{2}$

Used formulae :—

• (a+b)(a-b) = a² - b².

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# Brainly

If x = 1/√3-√2, prove that x³ + 1/x³ +2(x² + 1/x²)-9(x +1/x) = 20...

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