Question

Rationalize the denominator 3/(sqrt5+sqrt2)

Answer 1

ANSWER

Rationalizing the denominator

For this question,

⇒$\rm\frac{3}{\sqrt5+\sqrt2}$

⇒$\rm\frac{ 3 } { \sqrt5+\sqrt2 } * \frac { \sqrt5-\sqrt2 } { \sqrt5-\sqrt2 }$

⇒$\rm\frac{ 3\sqrt5-3\sqrt2 } { 5-2 }$

⇒$\boxed{\rm\frac{ 3\sqrt5-3\sqrt2 } { 3 }}$

Answer 2

Answer

As per your question we need to rationalize the denominator.

While Rationalizing we need to apply some property , so that the denominator becomes a rational number.

Here we will multiply the fraction by $</u></em><em><u>\boxed</u></em><em><u>{</u></em><em><u> \rm \frac { \sqrt5 - \sqrt2 } { \sqrt5 - \sqrt2 } </u></em><em><u>}</u></em><em><u>$

$\implies \rm \frac { 3 } { \sqrt5 + \sqrt2 }$ × $\rm \frac { \sqrt5 - \sqrt2 } { \sqrt5 - \sqrt2 }$

$\implies \rm \frac { 3\sqrt5 - 3\sqrt2 } { 5 - 2 }$

$\implies \boxed{\boxed{\rm \frac { 3 \sqrt5 - 3\sqrt2} { 3 }} }$