Answer:
You should multiply the expression by [tex]\frac{\sqrt{13}-\sqrt{11}}{\sqrt{13}-\sqrt{11}}[/tex]
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 [tex]\frac{2}{\sqrt{13}+\sqrt{11}}[/tex]
Consider the denominator:
From the above, we can conclude that the conjugate of [tex]\sqrt{13}+\sqrt{11}[/tex] is [tex]\sqrt{13}-\sqrt{11}[/tex]
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 [tex]\frac{\sqrt{13}-\sqrt{11}}{\sqrt{13}-\sqrt{11}}[/tex] in order to rationalize the denominator
Hope this helps :)
Answer:
[tex] \frac { \sqrt { 13 } - \sqrt { 11 } } { \sqrt { 13 } - \sqrt { 11 } } [/tex]
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:
[tex] \frac { 2 } { \sqrt { 13 } + \sqrt { 11 } } [/tex]
To rationalize its denominator, we must multiply it with its conjugate.
For the denominator of the given expression, its conjugate would be [tex] \sqrt { 13 } - \sqrt { 11 } [/tex].
So to rationalize the expression, we would multiply it with:
[tex] \frac { \sqrt { 13 } - \sqrt { 11 } } { \sqrt { 13 } - \sqrt { 11 } } [/tex]
