# Cube of Rational Numbers

Cube of Rational numbers : In the previous sections, we have learnt about the cubes of natural numbers and negative integers. Similarly, we define the cubes of rational numbers which is not an integer as given below.**Rational Number's cube**

Let a = m /n be a rational number

(m, n are non zero integers such that n ≠ + or – 1) other than an integer, then the cube of a is defined as

a

^{3}= a x a x a or

(m/n)

^{3}= m/n x m/n x m/n = m

^{3}/ n

^{3}

**Examples :**

1) Find (2/3)

^{3}

**Solution:**

(2/3)

^{3}= 2

^{3}/3

^{3}= 2 x 2 x 2/ 3 x 3 x 3 = 8 /27

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2) Find

**(5**2⁄7)

^{3}

**Solution :**

**5**2⁄7 = 37/7

= 37

^{3}/7

^{3}

= 37 x 37 x 37/ 7 x 7 x 7

= 50653/343

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3) Find

**(3**1⁄10)

^{3}

**Solution :**

**3**1⁄10 = 31/10

= 31

^{3}/10

^{3}

= 31 x 31 x 31/ 10 x 10 x 10

= 29791/1000

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4) Find (-6/11)

^{3}

**Solution:**

(-6/11)

^{3}= (-6)

^{3}/11

^{3}

= (-6) x (-6) x (-6)/ 11 x 11 x 11

= -216 /1331

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5) Find (-1/10)

^{3}

**Solution:**

(-1/11)

^{3}= (-1)

^{3}/10

^{3}

= (-1) x (-1) x (-1)/ 10 x 10 x 10

= -1 /1000

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6) Find (a/8)

^{3}

**Solution:**

(a/8)

^{3}= (a)

^{3}/8

^{3}

= (a) x (a) x (a)/ 8 x 8 x 8

= a

^{3}/512

**Cube -Cube Roots**

• Cube-Numbers

• Perfect- Cube

• Properties : Cube

• Cube - Column method

• Negative numbers-cube

• Cube of Rational numbers

• Cube-Root

• Finding cube-root by Prime Factorization

• Cube- root of Rational numbers

• Estimating cube -root

• Cube-Numbers

• Perfect- Cube

• Properties : Cube

• Cube - Column method

• Negative numbers-cube

• Cube of Rational numbers

• Cube-Root

• Finding cube-root by Prime Factorization

• Cube- root of Rational numbers

• Estimating cube -root

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