Algebra - Radicals (Practice Problems)

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Section 1.3 : Radicals

For problems 1 – 4 write the expression in exponential form.

$\sqrt[7]{y}$ Solution
$\sqrt[3]{{{x^2}}}$ Solution
$\sqrt[6]{{ab}}$ Solution
$\sqrt {{w^2}{v^3}}$ Solution

For problems 5 – 7 evaluate the radical.

$\sqrt[4]{{81}}$ Solution
$\sqrt[3]{{ - 512}}$ Solution
$\sqrt[3]{{1000}}$ Solution

For problems 8 – 12 simplify each of the following. Assume that x, y and z are all positive.

$\sqrt[3]{{{x^8}}}$ Solution
$\sqrt {8{y^3}}$ Solution
$\sqrt[4]{{{x^7}{y^{20}}{z^{11}}}}$ Solution
$\sqrt[3]{{54{x^6}{y^7}{z^2}}}$ Solution
$\sqrt[4]{{4{x^3}y}}\,\,\sqrt[4]{{8{x^2}{y^3}{z^5}}}$ Solution

For problems 13 – 15 multiply each of the following. Assume that x is positive.

$\sqrt x \left( {4 - 3\sqrt x } \right)$ Solution
$\left( {2\sqrt x + 1} \right)\left( {3 - 4\sqrt x } \right)$ Solution
$\left( {\sqrt[3]{x} + 2\,\,\sqrt[3]{{{x^2}}}} \right)\left( {4 - \sqrt[3]{{{x^2}}}} \right)$ Solution

For problems 16 – 19 rationalize the denominator. Assume that x and y are both positive.

$\displaystyle \frac{6}{{\sqrt x }}$ Solution
$\displaystyle \frac{9}{{\sqrt[3]{{2x}}}}$ Solution
$\displaystyle \frac{4}{{\sqrt x + 2\sqrt y }}$ Solution
$\displaystyle \frac{{10}}{{3 - 5\sqrt x }}$ Solution