Expressions with exponents and radicals

1003158601

Level:

The number

\sqrt[5]{9}

is bigger than:

3^{0.3}

\sqrt{3}

\sqrt[9]{81}

3

1003158602

Level:

a = \frac{1}{\sqrt{3} - 1}

and

b = \frac{1}{\sqrt{5} - 1} - \frac{2}{\sqrt{5}} + 1

, then:

a > b

a < b

a = b

a = - b

1003158603

Level:

After rationalizing the denominator

\frac{\sqrt{\sqrt{13} + \sqrt{12}}}{\sqrt{\sqrt{13} - \sqrt{12}}}

we get:

\sqrt{13} + 2 \sqrt{3}

\sqrt{13} - \sqrt{12}

1

25

1003158604

Level:

After rationalizing the denominator

\frac{4}{1 - \sqrt{2} + \sqrt{3}}

we get:

\sqrt{6} - \sqrt{2} + 2

- 4

\sqrt{6} - \sqrt{2}

1 + \sqrt{2} - \sqrt{3}

1003158605

Level:

Using the formula for factoring

a^{3} - b^{3}

to rationalize the denominator of

\frac{2}{\sqrt[3]{25} + \sqrt[3]{15} + \sqrt[3]{9}}

you get:

\sqrt[3]{5} - \sqrt[3]{3}

2

2 \sqrt[3]{49}

2 (\sqrt[3]{25} - \sqrt[3]{15 - \sqrt[3]{9}})

1003158606

Level:

Using the formula for factoring

a^{3} - b^{3}

to find the multiplicative inverse of

x = \sqrt[3]{3} - \sqrt[3]{4}

you get:

- \sqrt[3]{9} - \sqrt[3]{12} - \sqrt[3]{16}

\sqrt[3]{9} - \sqrt[3]{12} + \sqrt[3]{16}

\sqrt[3]{3} - \sqrt[3]{4}

\sqrt[3]{4} - \sqrt[3]{3}

1003158607

Level:

As a result of this mathematical action

\sqrt[3]{{[{(\sqrt{2} + 1)}^{3} - {(\sqrt{2} - 1)}^{3}]}^{2} - 13^{2}}

we get:

3

\sqrt[3]{- 170}

\sqrt[3]{13}

\sqrt[3]{- 168}

1003158608

Level:

As a result of this mathematical action

\frac{1}{\sqrt{2} + 1} + \frac{1}{\sqrt{3} + \sqrt{2}} + \frac{1}{\sqrt{4} + \sqrt{3}} + \dots + \frac{1}{\sqrt{100} + \sqrt{99}}

we get:

9

12

100

99

1003158609

Level:

Choose the correct relation.

\frac{4^{2 \sqrt{3}} \cdot 8}{16^{\sqrt{3} + 1}} = \frac{1}{2}

\frac{9^{2 \sqrt{5}} \cdot 27^{\frac{1}{3}}}{81^{1 - \sqrt{5}}} = \frac{1}{27}

\frac{π^{1 - \sqrt{2}} \cdot π^{1 + \sqrt{2}}}{π^{2}} < \frac{1}{π^{3}}

\frac{2^{2 π} \cdot 9^{π}}{36^{π - 1}} < 6

1003164001

Level:

After simplifying the expression

\sqrt[3]{5 \sqrt{2} + 7} - \sqrt[3]{5 \sqrt{2} - 7}

we get:

2

2 \sqrt[3]{57}

1

2 \sqrt[3]{97}

Expressions with exponents and radicals

1003158601

1003158602

1003158603

1003158604

1003158605

1003158606

1003158607

1003158608

1003158609

1003164001

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