Basic Math Examples

$(\sqrt{\frac{2 + \sqrt{3}}{2 - \sqrt{3}}}) (\sqrt{\frac{2 - \sqrt{3}}{2 + \sqrt{3}}})$

Step 1

Combine using the product rule for radicals.

$\sqrt{\frac{2 + \sqrt{3}}{2 - \sqrt{3}} \cdot \frac{2 - \sqrt{3}}{2 + \sqrt{3}}}$

Step 2

Multiply $\frac{2 + \sqrt{3}}{2 - \sqrt{3}}$ by $\frac{2 - \sqrt{3}}{2 + \sqrt{3}}$ .

$\sqrt{\frac{(2 + \sqrt{3}) (2 - \sqrt{3})}{(2 - \sqrt{3}) (2 + \sqrt{3})}}$

Step 3

Reduce the expression $\frac{(2 + \sqrt{3}) (2 - \sqrt{3})}{(2 - \sqrt{3}) (2 + \sqrt{3})}$ by cancelling the common factors.

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Step 3.1

Cancel the common factor.

$\sqrt{\frac{(2 + \sqrt{3}) (2 - \sqrt{3})}{(2 - \sqrt{3}) (2 + \sqrt{3})}}$

Step 3.2

Rewrite the expression.

$\sqrt{\frac{2 - \sqrt{3}}{2 - \sqrt{3}}}$

Step 4

Cancel the common factor of $2 - \sqrt{3}$ .

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Step 4.1

Cancel the common factor.

$\sqrt{\frac{2 - \sqrt{3}}{2 - \sqrt{3}}}$

Step 4.2

Rewrite the expression.

$\sqrt{1}$

Step 5

Any root of $1$ is $1$ .

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Step 5.1

Cancel the common factor.

$\frac{2 - \sqrt{3}}{2 - \sqrt{3}}$

Step 5.2

Rewrite the expression.

$1$