Question

rationalize the denominator√3+√2
√3-√2​

Answer 1

Answer:

5+2√6

Step-by-step explanation:

multiply numerator and denominator by √3+√2

Answer 2

Correct question:

Rationalize the denominator√3 + √2/√3 - √2

Answer:

5 + 2√6

Step-by-step explanation:

Rationalize the denominator means making the denominator a rational number. In order to rationalise the denominator, we multiply the given fraction with the rationalising factor of the denominator with both the numerator and the denominator of the given fraction.

Here, we have to rationalise the denominator of :

$\longmapsto \rm { \dfrac{\sqrt{3} + \sqrt{2}}{\sqrt{3} - \sqrt{2}} }$

The denominator of the given fraction is in the form of (a - b). Rationalising factor of a term means changing the sign to its opposite sign, Rationalising factor of (a - b) is (a + b). So, the rationalising factor of (√3 - √2) is (√3 + √2). Multiplying (√3 + √2) with both the numerator and the denominator.

$\longmapsto \rm { \dfrac{\sqrt{3} + \sqrt{2}}{\sqrt{3} - \sqrt{2}} \times }\dfrac{\sqrt{3} + \sqrt{2}}{\sqrt{3} + \sqrt{2} }$

Rearranging the terms.

$\longmapsto \rm { \dfrac{(\sqrt{3} + \sqrt{2})( \sqrt{3} + \sqrt{2)} }{(\sqrt{3} - \sqrt{2})( \sqrt{3} + \sqrt{2})} }$

Multiplying √3 + √2 with the terms in the brackets in the numerator & and using the identity given below in the numerator.

• (a - b)(a + b) = a² - b²

Simplifying further,

$\longmapsto \rm { \dfrac{{5 + 2\sqrt{6}} }{(\sqrt{3} - \sqrt{2})( \sqrt{3} + \sqrt{2})} }$

$\longmapsto \rm { \dfrac{{5 + 2\sqrt{6}} }{( { \sqrt{3})}^{2} - {(\sqrt{2})}^{2} } }$

Putting the values of squares of the numbers in the denominator.

$\longmapsto \rm { \dfrac{{5 + 2\sqrt{6}} }{ 3 - 2} }$

Subtracting the numbers in the denominator,

$\longmapsto \rm { \dfrac{{5 + 2\sqrt{6}} }{ 1}}$

And now, This fraction can be written as,

$\longmapsto \rm {5 + 2\sqrt{6}}$

∴ Hence, Denominator is rationalised !