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Definition of cube root of rational numbers : If x and a are two rational numbers such that x∛a = x

We know that,

(3/4)

(-4/11)

So in order to find the cube-root of rational-numbers we use the following :

For any rational number a/b, we have

1) ∛(27/8)

∛(27/8) = (∛27)/(∛8)

= (∛3 x 3 x 3)/(∛2 x 2 x 2 )

∛(27/8) = 3/2

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2) ∛(-64/125)

∛(-64/125) = (∛-64)/(∛125)

= (∛-4 x -4 x -4)/(∛5 x 5 x 5 )

∛(-64/125) = -4/5

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3) ∛(1.331)

∛(1.331) = ∛(1331/1000)

∛(1331/1000) = (∛1331)/(∛1000)

= (∛11 x 11 x 11)/(∛10 x 10 x 10 )

∛(1.331) = 11/10

∛(1.331) = 1.1

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4) ∛(0.008)

∛(0.008) = ∛(8/1000)

∛(8/1000) = (∛8)/(∛1000)

= (∛2 x 2 x 2)/(∛10 x 10 x 10 )

∛(0.008) = 2/10

∛(0.008)= 0.2

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5)∛(0.125)

∛(0.125) = ∛(125/1000)

∛(125/1000) = (∛125)/(∛1000)

= (∛5 x 5 x 5)/(∛10 x 10 x 10 )

∛(0.125) = 5/10

∛(0.125)= 0.5

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6)∛(216/343)

∛(216/343) = (∛216)/(∛343)

= (∛6 x 6 x 6)/(∛7 x 7 x 7 )

∛(216/343) = 6/7

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7)∛(1000/8)

∛(1000/8) = (∛1000)/(∛8)

= (∛10 x 10 x 10)/(∛2 x 2 x 2 )

∛(1000/8) = 10/8

∛(1000/8)= 5/4

• Cube of Numbers

• Perfect Cube

• Properties of Cube

• Cube by Column method

• Cube of Negative numbers

• Cube of Rational numbers

• Cube Root

• Finding cube root by Prime Factorization

• Cube root of Rational numbers

• Estimating cube root

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