Expressions with exponents and radicals

1003099501

Level:

Let

x = 4^{- 1} + 4^{- \frac{1}{2}} - {(\frac{\sqrt{2}}{2})}^{2}

. Which of the following inequalities is true?

x \geq 2^{- 2}

x < 4^{- 1}

x > 2

x \leq 4^{- 3}

1003099502

Level:

Simplify the fraction

\frac{\sqrt[8]{9} \cdot \sqrt[12]{27} \cdot \sqrt[4]{14}}{\sqrt[4]{42}}

\sqrt[4]{3}

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

1

3

1003099503

Level:

Let

a = 2 \sqrt{7} + \sqrt{5}

and

b = \frac{1}{\sqrt{7} - \sqrt{5}}

. Choose the right relation between

a

and

b

a > b

a = b

a < b

a + b = 0

1003099506

Level:

The additive inverse of

\frac{1}{5 - 2 \sqrt{5}}

is:

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

\frac{- 1}{2 \sqrt{5} - 5}

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

5 - 2 \sqrt{5}

1003099507

Level:

The multiplicative inverse of

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

is:

\frac{1}{\sqrt{3} + 1}

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

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

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

1003099510

Level:

What is the value of

\sqrt[4]{2 \sqrt{2}} \sqrt[8]{32}

2

2^{\frac{1}{2}}

2^{\frac{3}{4}}

2^{0}

1003099605

Level:

Simplifying

{(\sqrt[3]{3 \sqrt{9}})}^{\frac{3}{2}} \sqrt{9^{- 1}}

we get:

1

3 \sqrt[6]{3}

3 \sqrt[3]{3}

3

1003099606

Level:

Calculate the value of the expression

\frac{2 a + 12}{- a^{2}}

for

a = - 2 \sqrt{3}

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

4 \sqrt{3} - 1

\frac{- \sqrt{3} + 3}{3}

- 4 \sqrt{3} + 1

1003099608

Level:

Choose the correct statement about the number

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

It is a rational number.

It is an irrational number.

It is greater than

\sqrt{2}

It is a positive integer.

1003099609

Level:

Complete the sentence to get a true statement: The numbers

- \frac{\sqrt{3}}{6} - \frac{1}{2}

and

\sqrt{3} - 3

are ...

multiplicative inverses of each other.

equal.

rational numbers.

additive inverses of each other.

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Expressions with exponents and radicals

1003099501

1003099502

1003099503

1003099506

1003099507

1003099510

1003099605

1003099606

1003099608

1003099609

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