Question

What is the following quotient? StartFraction 2 Over StartRoot 13 EndRoot StartRoot 11 EndRoot EndFraction.

Answer 1

Function assigns one element of one set to the other specific element of another set. The quotient of the fraction $\dfrac{2}{\sqrt{13}+\sqrt{11}}$ is ${\sqrt{13}-\sqrt{11}}$.

What is a Function?

A function assigns the value of each element of one set to the other specific element of another set.

As the fraction is given to us,

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

Rationalizing the fraction we will get,

$=\dfrac{2}{\sqrt{13}+\sqrt{11}} \times \dfrac{{\sqrt{13}-\sqrt{11}}}{{\sqrt{13}-\sqrt{11}}}\\\\= \dfrac{2({\sqrt{13}-\sqrt{11}})}{(\sqrt{13})^2-(\sqrt{11})^2}\\\\= \dfrac{2({\sqrt{13}-\sqrt{11}})}{13-11}\\\\=\dfrac{2({\sqrt{13}-\sqrt{11}})}{2}$

Now, if we divide the numerator by the denominator to get the quotient we will get,

$= \dfrac{2({\sqrt{13}-\sqrt{11}})}{2}\\\\={2({\sqrt{13}-\sqrt{11}})}\div 2\\\\={\sqrt{13}-\sqrt{11}}$

Hence, the quotient of the fraction $\dfrac{2}{\sqrt{13}+\sqrt{11}}$ is ${\sqrt{13}-\sqrt{11}}$.

Learn more about Function:

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Answer 2

The quotient of the given number start Fraction 2 over start root 13 end root start root 11 end root end Fraction.

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

What is the quotient?

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,

$q=\dfrac{a}{b}$

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,

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

Let the quotient of this division is n. Therefore,

$n=\dfrac{2}{\sqrt{13}+\sqrt{11}}$

By rationalizing the denominator, we get,

$n=\dfrac{2}{\sqrt{13}+\sqrt{11}}\times\dfrac{\sqrt{13}-\sqrt{11}}{\sqrt{13}-\sqrt{11}}\\n=\dfrac{2(\sqrt{13}-\sqrt{11})}{(\sqrt{13})^2-(\sqrt{11})^2}\\n=\dfrac{2(\sqrt{13}-\sqrt{11})}{13-11}\\\\n=\dfrac{2(\sqrt{13}-\sqrt{11})}{2}\\n=\sqrt{13}-\sqrt{11}$

Hence, the quotient of the given number start Fraction 2 Over Start Root 13 End Root Start Root 11 End Root End Fraction.

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

Learn more about the quotient here;

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