9000010510
Level:
B
For \(x\in \mathbb{R}\),
\(x > 0\),
simplify the following expression.
\[
\root{3}\of{x} : \root{6}\of{x}
\]
\(\root{6}\of{x}\)
\(\root{}\of{x}\)
\(\root{3}\of{x^{2}}\)
\(x\)
Expressions with exponents and radicals
9000013501
Level:
B
Write the expression \(2^{\frac{3}
{4} }\)
in an equivalent form which does not contain a rational exponent.
\(\root{4}\of{2^{3}}\)
\(\root{4}\of{2}\)
\(\root{3}\of{2^{4}}\)
\(\root{4}\of{3^{2}}\)
9000013504
Level:
B
Simplify \(\sqrt{\root{4}\of{25}}\).
\(\root{4}\of{5}\)
\(\root{8}\of{5}\)
\(\root{4}\of{25}\)
\(\sqrt{5}\)
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.
\(20\root{3}\of{2}\)
\(10\root{3}\of{4}\)
\(100\root{3}\of{2}\)
\(4\root{3}\of{10}\)
9000013507
Level:
B
Simplify \(\root{4}\of{16\cdot 81}\).
\(6\)
\(36\)
\(\sqrt{6}\)
\(\root{4}\of{6}\)
9000013509
Level:
A
Simplify the expression \((1 + \sqrt{2})^{2}\).
\(3 + 2\sqrt{2}\)
\(3\)
\(3 - 2\sqrt{2}\)
\(3 + \sqrt{2}\)