Question

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Answer 1

$\huge\text{Question}$

By which smallest number should we divide the following numbers to make them perfect cubes ? Find the cube root of the perfect cube .

(i) 6655

Prime factorising 6655, we get,

6655 = 11 × 11 × 11 × 5

6655 = 11³ × 5¹

We know, a perfect cube has multiples of 3 as powers of prime factors. Here, we can see that power of 3 is 3 and power of 5 is 1.

so , The smallest number 5 should be divided by 6655 to make it perfect cube .

6655 ÷ 5 = 1331

Cube root of 1331 = 11

(ii) 31944

Prime factorising 31944, we get,

31944 = 2 × 2 × 2 × 3 × 11 × 11 × 11

31944 = 2³ × 3¹ × 11³

We know, a perfect cube has multiples of 3 as powers of prime factors. Here, we can see that power of 2 is 3 and power of 3 is 1 and the power of 11 is 3.

so , The smallest number 3 should be divided by 31944 to make it perfect cube .

31944 ÷ 3 = 10648

Cube root of 10648 = 22

(iii) 200704

Prime factorising 6655, we get,

200704 = 2× 2 ×2 ×2 ×2× 2× 2× 2× 2× 2× 2× 2× 7× 7

200704 = 2³ × 2³ × 2³ × 2³ × 7²

We know, a perfect cube has multiples of 3 as powers of prime factors. Here, we can see that power of all 2 is 3 and power of 7 is 2.

so , The smallest number 49 should be divided by 200704 to make it perfect cube .

200704 ÷ 49 = 4096

Cube root of 4096 = 16

(iv) 64827

Prime factorising 64827, we get,

64827 = 3 × 3 × 3 × 7 × 7 × 7 ×7

64827 = 3³ × 7³ × 7¹

We know, a perfect cube has multiples of 3 as powers of prime factors. Here, we can see that power of 3 is 3 and power of 7 is 3 and the power of other 7 is 1.

so , The smallest number 7 should be divided by 64827 to make it perfect cube .

64827 ÷ 7 = 9261

Cube root of 9261 = 21

(v) 163840

Prime factorising 163840, we get,

163840 = 2 × 2 × 2 × 2× 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 2 × 5

163840 = 2³ × 2³ × 2³ × 2³× 2³ × 5¹

We know, a perfect cube has multiples of 3 as powers of prime factors. Here, we can see that power of all 2 is 3 and power of 5 is 1.

so , The smallest number 5 should be divided by 163840 to make it perfect cube .

163840 ÷ 5 = 32768

Cube root of 32768 = 32

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$\huge\text{Question}$

find the cube root of the following :

(i) (-343) = (-7)

(ii) (-1331) = (-11)

(iii) (-3375) = (-15)

(iv) (-32768) = (-32)

(v) (-4913) = (-17)

Answer 2

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