Resources

Resources

Bytelearn - cat image with glasses

AI tutor

Welcome to Bytelearn!

Let’s check out your problem:

(sqrt11-sqrt3)/(sqrt11+sqrt3)

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

View step-by-step help

View step-by-step help

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. $\newline$ = $\frac{8}{11 - 3}$ $\newline$ = $\frac{8}{8}$ $\newline$ = $1$

More problems from Simplify radical expressions involving fractions

Question

\newline

\sqrt{\frac{9}{25}}

\newline

Posted 5 months ago

Question

Multiply. Write your answer in simplest form.

\newline

\sqrt{15} \times \sqrt{2}

\newline

Posted 5 months ago

Question

\newline

\sqrt{125}

Posted 7 months ago

Question

Add. Write your answer in simplest form.

\newline

-6\sqrt{3} + 7\sqrt{3}

\newline

Posted 5 months ago

Question

Multiply. Write your answer in simplest form.

\newline

-\sqrt{2}(5 - \sqrt{5})

Posted 5 months ago

Question

Simplify. Rationalize the denominator.

\newline

`(-7)/(2 + \sqrt{5}\)`

\newline

Posted 5 months ago

Question

Simplify. Assume

x

is greater than or equal to zero.

\newline

\sqrt{20x^3}

Posted 5 months ago

Question

\sqrt{\frac{49}{81}}=

Posted 3 months ago

Question

\sqrt[3]{512}=

Posted 2 months ago

Question

\sqrt[3]{1000}=

Posted 2 months ago

Related topics

Algebra - Order of Operations Algebra - Distributive Property `X` and `Y` Axes Geometry - Scalene Triangle Common Multiple Geometry - Quadrant