Expressions with exponents and radicals

1003032107

Level:

The average distance of the Moon from Earth is

3.84 \cdot 10^{8} m

, and the average distance of Earth from the Sun is

1.5 \cdot 10^{11} m

. How many times further is it from Earth to the Sun than from Earth to the Moon?

about

390

times

about

39

times

3 900

times

about

4

times

1003032110

Level:

Calculate

\sqrt[3]{- \frac{8}{125}} - \sqrt[3]{- 2 \frac{10}{27}}

\frac{14}{15}

- \frac{2}{5}

1 \frac{2}{97}

2 \frac{18}{152}

1003034104

Level:

Evaluating the expression

\frac{1}{3} \sqrt[3]{4} \cdot \sqrt[3]{2}

we get:

\frac{2}{3}

\frac{8}{3}

\frac{2}{6}

\frac{3}{3}

1003034106

Level:

The value of the expression

\frac{\sqrt[3]{81}}{\sqrt[3]{3}}

is:

3

3 \sqrt{3}

\frac{9}{\sqrt[3]{3}}

27

1003099207

Level:

Rationalize the denominator of

\frac{5}{\sqrt{2}}

2.5 \sqrt{2}

2.5

\frac{5}{4} \sqrt{2}

5 \sqrt{2}

1003099208

Level:

Rationalize the denominator of

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

\sqrt{2} + 1

2

2 \sqrt{2}

2 \sqrt{2} + 1

1003099209

Level:

Rationalize the denominator of

\frac{1}{\sqrt[3]{2}}

0.5 \sqrt[3]{4}

0.5

0.5 \sqrt[3]{2}

0.5 \sqrt{2}

1003099210

Level:

Write the fraction

\frac{\sqrt[3]{2}}{\sqrt[3]{3}}

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

\frac{\sqrt[3]{18}}{3}

\frac{\sqrt[3]{6}}{3}

\frac{2}{3}

\sqrt[3]{6}

1003099211

Level:

Write the fraction

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

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

\frac{2 \sqrt{3} - 3}{6}

0

1

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

1003099504

Level:

Rationalizing the denominator

\frac{1}{\sqrt{5} + \sqrt{7}}

we get:

\frac{\sqrt{7} - \sqrt{5}}{2}

\frac{\sqrt{5} + \sqrt{7}}{2}

\frac{\sqrt{5} - \sqrt{7}}{2}

\frac{- \sqrt{7} - \sqrt{5}}{2}

Expressions with exponents and radicals

1003032107

1003032110

1003034104

1003034106

1003099207

1003099208

1003099209

1003099210

1003099211

1003099504

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