Question

Rationalized 1/√7-2 please help me please solve it​

Answer 1

Given :–

• An equation, $\dfrac{1}{\sqrt{7} - 2}$

Required :–

• Rationalise the given equation.

Solution :–

Given,

• $\dfrac{1}{ \sqrt{7 } - 2}$

Now, multiply the reciprocal of the denominator (√7 – 2) by the given equation.

I.e.,

Reciprocal :– Changing of signs. like, positive to negative / negative to positive.

Reciprocal of the denominator (√7 – 2) is √7 + 2.

So,

$\mapsto \dfrac{1}{ \sqrt{7} - 2} \times \dfrac{ \sqrt{7} + 2}{ \sqrt{7} + 2}$

$\mapsto \dfrac{1( \sqrt{7} + 2) }{ (\sqrt{7} - 2)( \sqrt{7} + 2) }$

Using identity :–

(a – b) (a + b) = a² – b²

So,

$\mapsto \dfrac{ \sqrt{7} + 2 }{ {( \sqrt{7} )}^{2} - {(2)}^{2} }$

We know that,

• Saare root cuts the powers.

$\mapsto \dfrac{ \sqrt{7} + 2}{7 - 4}$

$\mapsto \dfrac{ \sqrt{7} + 2 }{3}$

Hence,

The rationalising of $\dfrac{1}{\sqrt{7} - 2}$ is $\dfrac{\sqrt{7} + 2}{3}$

Answer 2

Answer:

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