Question

Multiplying 3/sqrt 17 - sqrt 2 by which fraction will produce an equivalent fraction with a rational denominator

Answer 1

You you use the conjugate of  sqrt17 - sqrt 2  which is sqrt17 + sqrt2

so the fraction is   sqrt17 + sqrt2
                              ------------------
                             sqrt17 + sqrt2

Answer 2

Given radical expression: $\frac{3}{\sqrt{17}-\sqrt{2}}$.

We need to find the fraction by which fraction will produce an equivalent fraction with a rational denominator.

In the given expression, we have $\sqrt{17}-\sqrt{2}.$

Which is an irrational number in denominator.

In order to get rid irrational number from denominator and get a rational number in denominator, we need to multiply given expression by conjugate of the denominator.

The conjugate of $\sqrt{17}-\sqrt{2}$ is $\sqrt{17}+\sqrt{2}$.

Therefore, we need to multiply $\frac{3}{\sqrt{17}-\sqrt{2}}$ by $\frac{\sqrt{17}+\sqrt{2}}{\sqrt{17}+\sqrt{2}}$ fraction that will produce an equivalent fraction with a rational denominator.