# Cube of Rational Numbers

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**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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