Question

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Answer 1

ANSWER:

Given:

• √2 = 1.414
• √3 = 1.732

To Find:

• Value of 1/(√3 - √2)

Solution:

We need to find the value of,

$\implies\dfrac{1}{\sqrt3-\sqrt2}$

On rationalising,

$\implies\dfrac{1}{\sqrt3-\sqrt2}\times\dfrac{\sqrt3+\sqrt2}{\sqrt3+\sqrt2}$

So,

$\implies\dfrac{\sqrt3+\sqrt2}{(\sqrt3-\sqrt2)(\sqrt3+\sqrt2)}$

We know that,

$\hookrightarrow (a+b)(a-b)=a^2-b^2$

So,

$\implies\dfrac{\sqrt3+\sqrt2}{(\sqrt3-\sqrt2)(\sqrt3+\sqrt2)}$

$\implies\dfrac{\sqrt3+\sqrt2}{(\sqrt3)^2-(\sqrt2)^2}$

$\implies\dfrac{\sqrt3+\sqrt2}{3-2}$

$\implies\dfrac{\sqrt3+\sqrt2}{1}$

$\implies\sqrt3+\sqrt2$

Substituting the value of √2 & √3,

$\implies\sqrt3+\sqrt2$

$\implies 1.732+1.414$

$\implies 3.146$

Therefore,

$\implies\bf \dfrac{1}{\sqrt3-\sqrt2}= 3.146$

Answer 2

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