Question

Rationalise the denominators of the following.

(a) 1

√7+√6​

Answer 1

Step-by-step explanation:

Answer

7

−

6

1

Multiply numerator and denominator by

7

+

6

=

(

7

−

6

)(

7

+

6

)

1(

7

+

6

)

=

7−6

7

+

6

=

7

+

6

Answer 2

Answer:

$\frac{ \sqrt{7} - \sqrt{6} }{1}$

Step-by-step explanation:

Solution -

➠‎ ‎Let's rationalise the given irrational number.

$\frac{1}{ \sqrt{7} + \sqrt{6} } \\ \\ = \frac{1}{ \sqrt{7} + \sqrt{6} } \times \frac{ \sqrt{7} - \sqrt{6} }{ \sqrt{7} - \sqrt{6} } \\ \\ (a - {b)}^{2} = {(a - b)}(a + b) \\ \\ = ( \sqrt{7} - \sqrt{6} {)}^{2} \\ \\ = ( \sqrt{7} {)}^{2} - ( \sqrt{6} {)}^{2} \\ \\ = 7 - 6 \\ \\ = 1 \\ \\ = \frac{ \sqrt{7} - \sqrt{6} }{1}$