Cube Root of Rational Numbers

Definition of cube root of rational numbers : If x and a are two rational numbers such that x³ = a then we say that x is the cube root of a and we write
∛a = x

We know that,
(3/4)³ = 27/64 ⇒ ∛(27/64) = 3/4

(-4/11)³ = -64/1331 ⇒ ∛(-64/1331) = -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

∛(a/b) = (∛a)/(∛b)

Examples :

1) ∛(27/8)

Solution :

∛(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)

Solution :

∛(-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)

Solution :

∛(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)

Solution :

∛(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)

Solution :

∛(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)

Solution :

∛(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)

Solution :

∛(1000/8) = (∛1000)/(∛8)

= (∛10 x 10 x 10)/(∛2 x 2 x 2 )

∛(1000/8) = 10/8

∛(1000/8)= 5/4

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Cube and Cube Roots

• 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

From Cube root of rational-numbers to Exponents

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