Question

What is the following quotient 9+sqrt 2/4-sqrt 7

Answer 1

9 + √2 / 4 - √7

Multiply the numerator and denominator by the conjugate.

Exact form:

(36 + 9√ 7 + 4√2 + √14) / 9

or

about 7.69

:)))

Answer 2

$\frac{9+\sqrt{2}}{4-\sqrt{7}}$

multiply by the conjugate of denominator.

$=\frac{9+\sqrt{2}}{4-\sqrt{7}}* \frac{4+\sqrt{7}}{4+\sqrt{7}}$

$=\frac{(9+\sqrt{2})(4+\sqrt{7})}{(4-\sqrt{7})(4+\sqrt{7})}$

apply formula (a+b)(a-b)=a^2-b^2

$=\frac{(9+\sqrt{2})(4+\sqrt{7})}{(4^2-(\sqrt{7})^2)}$

$=\frac{(9+\sqrt{2})(4+\sqrt{7})}{16-7}$

$=\frac{(9+\sqrt{2})(4+\sqrt{7})}{9}$

$=\frac{36+9 \sqrt{7} +4 \sqrt{2} + \sqrt{14}}{9}$

Hence final answer is $\frac{36+9 \sqrt{7} +4 \sqrt{2} + \sqrt{14}}{9}$