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(sqrt11-sqrt3)/(sqrt11+sqrt3)

$\frac{\sqrt{11}-\sqrt{3}}{\sqrt{11}+\sqrt{3}}$

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Simplify radical expressions involving fractions

Full solution

Q.

\frac{\sqrt{11}-\sqrt{3}}{\sqrt{11}+\sqrt{3}}

Apply Difference of Squares: Step $1$ : Apply the difference of squares formula to simplify the expression. $\newline$ $\frac{\sqrt{11} - \sqrt{3}}{\sqrt{11} + \sqrt{3}}$ * $\frac{\sqrt{11} - \sqrt{3}}{\sqrt{11} - \sqrt{3}}$ $\newline$ = $\frac{\sqrt{11}^2 - \sqrt{3}^2}{\sqrt{11}^2 - \sqrt{3}^2}$
Calculate Squares: Step $2$ : Calculate the squares of $\sqrt{11}$ and $\sqrt{3}$ . $\newline$ $\sqrt{11}^2 = 11$ $\newline$ $\sqrt{3}^2 = 3$ $\newline$ $11 - 3 = 8$
Substitute Values: Step $3$ : Substitute the values back into the expression. $\newline$ = $\frac{8}{11 - 3}$ $\newline$ = $\frac{8}{8}$ $\newline$ = $1$

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