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Cube Roots

Cube root of perfect cubes

The product of the same three factors is called a perfect cube.

For example,
1 is a perfect cube because 1=1x1x1=13
8 is a perfect cube because 8=2x2x2=23
27 is a perfect cube because 27=3x3x3=33
64 is a perfect cube because 64=4x4x4=43
...

The cube root of a number is the opposite (or inverse) of cubing a number.

$\sqrt[3]{64}=4$     because 4x4x4=64

$\sqrt[3]{125}=5$     because 5x5x5=125

To find the cube root of a fraction, reduce the numerator and the denominator to perfect cubes is possible.

Find $\sqrt[3]{\frac{16}{250}}$

$\sqrt[3]{\frac{16}{250}}=\sqrt[3]{\frac{8}{125}}=\frac{\sqrt[3]{8}}{\sqrt[3]{125}}=\frac{2}{5}$

Find $\sqrt[3]{5\frac{23}{64}}$

$\sqrt[3]{5\frac{23}{64}}=\sqrt[3]{\frac{343}{64}}=\frac{\sqrt[3]{343}}{\sqrt[3]{64}}=\frac{7}{4}=1\frac{3}{4}$

Find $\sqrt[3]{343}$

Solution: