The quotient of the given number start Fraction 2 over start root 13 end root start root 11 end root end Fraction.
![\sqrt{13}-\sqrt{11}](https://tex.z-dn.net/?f=%5Csqrt%7B13%7D-%5Csqrt%7B11%7D)
<h3>What is the quotient?</h3>
Quotient is the resultant number which is obtained by dividing a number with another. Let a number a is divided by number b. Then the quotient of these two number will be,
![q=\dfrac{a}{b}](https://tex.z-dn.net/?f=q%3D%5Cdfrac%7Ba%7D%7Bb%7D)
Here, (a, b) are the real numbers.
The number Start Fraction 2 Over Start Root 13 End Root Start Root 11 End Root End Fraction given can be written as,
![\dfrac{2}{\sqrt{13}+\sqrt{11}}](https://tex.z-dn.net/?f=%5Cdfrac%7B2%7D%7B%5Csqrt%7B13%7D%2B%5Csqrt%7B11%7D%7D)
Let the quotient of this division is n. Therefore,
![n=\dfrac{2}{\sqrt{13}+\sqrt{11}}](https://tex.z-dn.net/?f=n%3D%5Cdfrac%7B2%7D%7B%5Csqrt%7B13%7D%2B%5Csqrt%7B11%7D%7D)
By rationalizing the denominator, we get,
![n=\dfrac{2}{\sqrt{13}+\sqrt{11}}\times\dfrac{\sqrt{13}-\sqrt{11}}{\sqrt{13}-\sqrt{11}}\\n=\dfrac{2(\sqrt{13}-\sqrt{11})}{(\sqrt{13})^2-(\sqrt{11})^2}\\n=\dfrac{2(\sqrt{13}-\sqrt{11})}{13-11}\\\\n=\dfrac{2(\sqrt{13}-\sqrt{11})}{2}\\n=\sqrt{13}-\sqrt{11}](https://tex.z-dn.net/?f=n%3D%5Cdfrac%7B2%7D%7B%5Csqrt%7B13%7D%2B%5Csqrt%7B11%7D%7D%5Ctimes%5Cdfrac%7B%5Csqrt%7B13%7D-%5Csqrt%7B11%7D%7D%7B%5Csqrt%7B13%7D-%5Csqrt%7B11%7D%7D%5C%5Cn%3D%5Cdfrac%7B2%28%5Csqrt%7B13%7D-%5Csqrt%7B11%7D%29%7D%7B%28%5Csqrt%7B13%7D%29%5E2-%28%5Csqrt%7B11%7D%29%5E2%7D%5C%5Cn%3D%5Cdfrac%7B2%28%5Csqrt%7B13%7D-%5Csqrt%7B11%7D%29%7D%7B13-11%7D%5C%5C%5C%5Cn%3D%5Cdfrac%7B2%28%5Csqrt%7B13%7D-%5Csqrt%7B11%7D%29%7D%7B2%7D%5C%5Cn%3D%5Csqrt%7B13%7D-%5Csqrt%7B11%7D)
Hence, the quotient of the given number start Fraction 2 Over Start Root 13 End Root Start Root 11 End Root End Fraction.
![\sqrt{13}-\sqrt{11}](https://tex.z-dn.net/?f=%5Csqrt%7B13%7D-%5Csqrt%7B11%7D)
Learn more about the quotient here;
brainly.com/question/673545