9000010504
Level:
A
For \(x\in \mathbb{R}\),
\(x > 0\),
simplify the following expression.
\[
\root{3}\of{x^{2}} : \root{3}\of{x}
\]
\(\root{3}\of{x}\)
\(x\)
\(1\)
\(\root{9}\of{x}\)
Expressions with exponents and radicals
9000010507
Level:
A
For \(x\in \mathbb{R}\),
\(x > 0\),
simplify the following expression.
\[
x^{3} : \root{}\of{x}
\]
\(x^{2}\root{}\of{x}\)
\(x^{3}\root{}\of{x}\)
\(\root{}\of{x^{3}}\)
\(\root{6}\of{x}\)
9000010509
Level:
A
For \(x\in \mathbb{R}\),
\(x > 0\),
simplify the following expression.
\[
x\cdot \root{3}\of{x^{11}}
\]
\(x^{4}\root{3}\of{x^{2}}\)
\(x^{11}\root{3}\of{x}\)
\(x^{12}\root{3}\of{x}\)
\(x\root{3}\of{x}\)
9000013505
Level:
A
Write the number \(3\root{3}\of{3}\)
in an equivalent form involving just radical of a single number or radical of a single
power.
\(\root{3}\of{81}\)
\(\sqrt{9}\)
\(\root{3}\of{27}\)
\(\root{3}\of{3^{2}}\)
9000013506
Level:
A
Write the number \(\root{3}\of{16000}\)
in an equivalent form with smallest possible number under the radical.
\(20\root{3}\of{2}\)
\(10\root{3}\of{4}\)
\(100\root{3}\of{2}\)
\(4\root{3}\of{10}\)
9000013508
Level:
A
Write the fraction \(\frac{\sqrt{7}}
{\sqrt{3}}\)
in an equivalent form which does not contain radical in the denominator.
\(\frac{\sqrt{21}}
{3} \)
\(\frac{\sqrt{10}}
{3} \)
\(\frac{\sqrt{7}+\sqrt{3}}
{3} \)
\(\frac{7}
{3}\)
9000013509
Level:
A
Simplify the expression \((1 + \sqrt{2})^{2}\).
\(3 + 2\sqrt{2}\)
\(3\)
\(3 - 2\sqrt{2}\)
\(3 + \sqrt{2}\)
9000013510
Level:
A
Write the fraction \(\frac{1}
{1+\sqrt{2}}\)
in an equivalent form which does not contain radical in the denominator.
\(\sqrt{2} - 1\)
\(\sqrt{2}\)
\(\frac{1}
{\sqrt{2}}\)
\(1 -\sqrt{2}\)
1003032101
Level:
B
The product of the numbers \( \left(\sqrt[3]{25}\cdot\sqrt5\right)^{-1} \) and \( \sqrt[6]5\cdot625^{\frac14} \) equals:
\( 1 \)
\( \frac15 \)
\( \sqrt5 \)
\( 5 \)
1003032102
Level:
B
The number \( \frac{\left(1.4\cdot10^{6}\right)\cdot\left(5.4\cdot10^{-8}\right)}{\left(3.6\cdot10^{-3}\right)\left(3.5\cdot10^{-4}\right)} \) is \( k \)-times bigger than the number \( 3000 \) for:
\( k=20 \)
\( k=2 \)
\( k=6 \)
\( k=10 \)