Expressions with exponents and radicals

9000013507

Level:

Simplify

\sqrt[4]{16 \cdot 81}

6

36

\sqrt{6}

\sqrt[4]{6}

9000079207

Level:

Assuming

x \notin {0; 1; 3}

, simplify the following expression.

\frac{x^{2} - 9}{x^{2} - x} \cdot {(\frac{x^{2} - 3 x}{x - 1})}^{- 1}

\frac{x + 3}{x^{2}}

\frac{x - 3}{x^{2}}

\frac{x + 3}{2 x}

\frac{x + 3}{x}

1003034108

Level:

Give the result of the gradual exponentiation

{({({({(2)}^{2})}^{0})}^{3})}^{4}

1

0

4^{12}

2^{9}

1003109205

Level:

The bank offers a term deposit with annual interest rate of

0.9 %

. We need to tax our profits with the income tax of

15 %

. How many Euros are we going to have after five years of savings if the original deposit is

200

Euros?

207.77

209.36

371.8

209.16

207.65

1003118001

Level:

The number

3 \sqrt[3]{3} \cdot \sqrt[4]{3 \sqrt[3]{3}} \cdot \sqrt[5]{3 \sqrt[3]{3} \cdot \sqrt[4]{3 \sqrt[3]{3}}}

is equal to:

9

3

\sqrt{3}

\sqrt[3]{3}

1003118002

Level:

The number

\sqrt{7 - 4 \sqrt{3}} + \sqrt{7 + 4 \sqrt{3}}

is equal to:

4

\sqrt{14}

16

8 \sqrt{3}

1003118003

Level:

Give the multiplicative inverse of

\frac{\sqrt[3]{4} - \sqrt[3]{2}}{2}

2 \sqrt[3]{2} + 2 + \sqrt[3]{4}

\sqrt[3]{12} + 2 + \sqrt[3]{4}

2 \sqrt[3]{12} + 2 + \sqrt[3]{4}

\sqrt[3]{2} + 2 + \sqrt[3]{4}

1003118004

Level:

The number

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

equals:

\sqrt{2} - 1

1 - \sqrt{2}

\sqrt{2}

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

1003118006

Level:

Give the value of the expression

\sqrt{{(2 - \sqrt{7})}^{2}} - \sqrt{{(3 + \sqrt{7})}^{2}}

- 5

- 1

- 1 - 2 \sqrt{7}

- 5 + 2 \sqrt{7}

1003118007

Level:

Calculate the fourth power of the number

1 - \sqrt{2}

17 - 12 \sqrt{2}

17 - 4 \sqrt{2}

3 - 2 \sqrt{2}

9 - 4 \sqrt{2}

Expressions with exponents and radicals

9000013507

9000079207

1003034108

1003109205

1003118001

1003118002

1003118003

1003118004

1003118006

1003118007

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