9000010510 Level: BFor \(x\in \mathbb{R}\), \(x > 0\), simplify the following expression. \[ \root{3}\of{x} : \root{6}\of{x} \]\(\root{6}\of{x}\)\(\root{}\of{x}\)\(\root{3}\of{x^{2}}\)\(x\)
9000013501 Level: BWrite 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: BSimplify \(\sqrt{\root{4}\of{25}}\).\(\root{4}\of{5}\)\(\root{8}\of{5}\)\(\root{4}\of{25}\)\(\sqrt{5}\)
9000013505 Level: AWrite 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: AWrite the number \(\root{3}\of{16000}\) in an equivalent form with smallest possible number under the radical.\(20\root{3}\of{2}\)\(10\root{3}\of{4}\)\(100\root{3}\of{2}\)\(4\root{3}\of{10}\)
9000013509 Level: ASimplify the expression \((1 + \sqrt{2})^{2}\).\(3 + 2\sqrt{2}\)\(3\)\(3 - 2\sqrt{2}\)\(3 + \sqrt{2}\)
9000013508 Level: AWrite 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: AWrite 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: BFor \(x\in \mathbb{R}\), \(x > 0\), simplify the following expression. \[ \root{5}\of{x^{3}} : \root{3}\of{x} \]\(\root{15}\of{x^{4}}\)\(\root{5}\of{x}\)\(\root{3}\of{x^{2}}\)\(\root{5}\of{x^{2}}\)