Question

Rationalize the denominator! Question in the picture

Answer 1

Answer:

A

Step-by-step explanation:

$\frac{10}{9+\sqrt{7} }$

To rationalise the denominator multiply the numerator and denominator by the conjugate of the denominator.

the conjugate of 9 + $\sqrt{7}$ is 9 - $\sqrt{7}$

= $\frac{10(9-\sqrt{7}) }{(9+\sqrt{7})(9-\sqrt{7}) }$ ← expand denominator using FOIL

= $\frac{90-10\sqrt{7} }{81-7}$

= $\frac{90-10\sqrt{7} }{74}$ ( divide terms on numerator/ denominator by 2 )

= $\frac{45-5\sqrt{7} }{37}$ → A

Answer 2

Answer:

A$\frac{45-5\sqrt7}{37}$

Step-by-step explanation:

Easy. First let's multiply numerator and denominator by $9-\sqrt7$ since we will create a difference of squares to get rid of the root, then start doing the calculations

$\frac{10(9-\sqrt7)}{(9+sqrt7)(9-\sqrt7)}=\frac{10(9-\sqrt7)}{81-7} = \frac{10(9-\sqrt7)}{74} =\\\frac{5(9-\sqrt7)}{37}=\frac{45-5\sqrt7}{37}$