Expressions with exponents and radicals

9000013506

Level:

Write the number

\sqrt[3]{16000}

in an equivalent form with smallest possible number under the radical.

20 \sqrt[3]{2}

10 \sqrt[3]{4}

100 \sqrt[3]{2}

4 \sqrt[3]{10}

Level:

Simplify

\sqrt[4]{16 \cdot 81}

6

36

\sqrt{6}

\sqrt[4]{6}

Level:

Simplify the expression

(1 + \sqrt{2})^{2}

3 + 2 \sqrt{2}

3

3 - 2 \sqrt{2}

3 + \sqrt{2}

Level:

Write the fraction

\frac{\sqrt{7}}{\sqrt{3}}

in an equivalent form which does not contain radical in the denominator.

\frac{\sqrt{21}}{3}

\frac{\sqrt{10}}{3}

\frac{\sqrt{7} + \sqrt{3}}{3}

\frac{7}{3}

Level:

Write the fraction

\frac{1}{1 + \sqrt{2}}

in an equivalent form which does not contain radical in the denominator.

\sqrt{2} - 1

\sqrt{2}

\frac{1}{\sqrt{2}}

1 - \sqrt{2}