Question

To rationalize the denominator of 2/square 13+ squared 11 , you should multiply the expression by which fraction?

Answer 1

Answer:

$\frac { \sqrt { 13 } - \sqrt { 11 } } { \sqrt { 13 } - \sqrt { 11 } }$

Step-by-step explanation:

We are given the following expression and we are to determine the expression that we need to multiply it with in order to rationalize the denominator:

$\frac { 2 } { \sqrt { 13 } + \sqrt { 11 } }$

To rationalize its denominator, we must multiply it with its conjugate.

For the denominator of the given expression, its conjugate would be $\sqrt { 13 } - \sqrt { 11 }$.

So to rationalize the expression, we would multiply it with:

$\frac { \sqrt { 13 } - \sqrt { 11 } } { \sqrt { 13 } - \sqrt { 11 } }$

Answer 2

Answer:

You should multiply the expression by $\frac{\sqrt{13}-\sqrt{11}}{\sqrt{13}-\sqrt{11}}$

Explanation:

To rationalize any expression, you must multiply it by its conjugate. A conjugate is defined as a similar expression to the original one but with an opposite sign

This means that:

The conjugate of a + b would be a -  b

Now, the given expression is $\frac{2}{\sqrt{13}+\sqrt{11}}$

Consider the denominator:

From the above, we can conclude that the conjugate of $\sqrt{13}+\sqrt{11}$ is $\sqrt{13}-\sqrt{11}$

And, remember that we need to keep the value of the expression unchanged. This means that we must multiply both the numerator and the denominator by the same value

Therefore:

You should multiply the expression by $\frac{\sqrt{13}-\sqrt{11}}{\sqrt{13}-\sqrt{11}}$ in order to rationalize the denominator

Hope this helps :)