9000013506
Level:
A
Write the number \(\root{3}\of{16000}\)
in an equivalent form with smallest possible number under the radical.
\(20\root{3}\of{2}\)
\(10\root{3}\of{4}\)
\(100\root{3}\of{2}\)
\(4\root{3}\of{10}\)
Expressions with Exponents and Radicals
9000013507
Level:
B
Simplify \(\root{4}\of{16\cdot 81}\).
\(6\)
\(36\)
\(\sqrt{6}\)
\(\root{4}\of{6}\)
9000013509
Level:
A
Simplify the expression \((1 + \sqrt{2})^{2}\).
\(3 + 2\sqrt{2}\)
\(3\)
\(3 - 2\sqrt{2}\)
\(3 + \sqrt{2}\)
9000013508
Level:
A
Write the fraction \(\frac{\sqrt{7}}
{\sqrt{3}}\)
in an equivalent form which does not contain radical in the denominator.
\(\frac{\sqrt{21}}
{3} \)
\(\frac{\sqrt{10}}
{3} \)
\(\frac{\sqrt{7}+\sqrt{3}}
{3} \)
\(\frac{7}
{3}\)
9000013510
Level:
A
Write the fraction \(\frac{1}
{1+\sqrt{2}}\)
in an equivalent form which does not contain radical in the denominator.
\(\sqrt{2} - 1\)
\(\sqrt{2}\)
\(\frac{1}
{\sqrt{2}}\)
\(1 -\sqrt{2}\)
9000010505
Level:
B
For \(x\in \mathbb{R}\),
\(x > 0\),
simplify the following expression.
\[
\root{5}\of{x^{3}} : \root{3}\of{x}
\]
\(\root{15}\of{x^{4}}\)
\(\root{5}\of{x}\)
\(\root{3}\of{x^{2}}\)
\(\root{5}\of{x^{2}}\)
9000010501
Level:
A
For \(x\in \mathbb{R}\),
\(x > 0\),
simplify the following expression.
\[
\root{3}\of{x^{5}}
\]
\(x\root{3}\of{x^{2}}\)
\(x^{2}\root{3}\of{x^{2}}\)
\(x^{3}\root{3}\of{x^{2}}\)
\(x^{2}\root{5}\of{x^{3}}\)
9000010508
Level:
B
For \(x\in \mathbb{R}\),
\(x > 0\),
simplify the following expression.
\[
\root{3}\of{x^{2}}\cdot \root{5}\of{x^{4}}
\]
\(\root{15}\of{x^{22}}\)
\(\root{15}\of{x^{6}}\)
\(\root{15}\of{x^{8}}\)
\(x^{3}\root{15}\of{x}\)
9000010502
Level:
A
For \(x\in \mathbb{R}\),
\(x > 0\),
simplify the following expression.
\[
\root{3}\of{x^{5}}\cdot \root{3}\of{x^{4}}
\]
\(x^{3}\)
\(\root{3}\of{x^{12}}\)
\(\root{3}\of{x}\)
\(x\root{3}\of{x^{4}}\)
9000010509
Level:
A
For \(x\in \mathbb{R}\),
\(x > 0\),
simplify the following expression.
\[
x\cdot \root{3}\of{x^{11}}
\]
\(x^{4}\root{3}\of{x^{2}}\)
\(x^{11}\root{3}\of{x}\)
\(x^{12}\root{3}\of{x}\)
\(x\root{3}\of{x}\)