Question

Rationalise 6/√7+√5​

Answer 1

Answer:

3√7-3√5

Step-by-step explanation:

6/√7+√5

=6(√7-√5)/(√7+√5)(√7-√5)

=6√7-6√5/7-5

=6√7-6√5/2

=6(√7-√5)/2

=3√7-3√5

Answer 2

✦ $\large{\underline{\mathfrak{\blue{Rationalisation:}}}}$

= $\sf{\dfrac{6}{\sqrt{7} + \sqrt{5}}}$

= $\sf{\dfrac{6}{\sqrt{7} + \sqrt{5}}× \dfrac{\sqrt{7} - \sqrt{5}}{ \sqrt{7} - \sqrt{5}}}$

In the denominator we have (√7 + √5)(√7 - √5) which is similar to the identify (a + b)(a - b) = a² - b². So, use this identity in the denominator.

= $\sf{ \dfrac{6\sqrt{7} - 6\sqrt{5}}{ {7}^{2} - {5}^{2}}}$

= $\sf{ \dfrac{6\sqrt{7} - 6\sqrt{5}}{ {7} - {5}}}$

= $\sf{ \dfrac{6\sqrt{7} - 6\sqrt{5}}{ 2}}$

= $\sf{ \dfrac{2(3\sqrt{7} - 3\sqrt{5})}{ 2}}$

= 3√7 - 3√5

Yeah! That's the answer! :)