Question

Find the cube root of the following numbers by Prime Fractorisation Method: Q1. 64 Q2. 512 Q3. 10648 Q4. 27000 Q5. 15625 Q6. 13824 Q7. 110592 Q8. 46656 Q9. 175616 Q10. 91125

Answer 1

Answer:

In the prime factorization of a perfect cube the factors can be grouped such that is group contains 3 equal prime factors.

Hence, to find the cube root of perfect cube say  n , proceed as follows:

 

1. Find the prime factors of a given number n

2.Form groups of 3 factors such that all three factor in each group are equal.

3.Choose one factor from each group and find the product . This product is the required cube root.

 

If a group contains one or two equal factor only then a given number cannot be a perfect cube.

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Solution:

[ prime factorization is in the attachments]

i)  64 = 2 x 2 x 2 x 2 x 2 x 2

= 2³ x 2³

³√64 =   2×2=4

ii) 512 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2

= 2³x 2³ x 2³

³√512 =   2×2×2=8

iii)  10648 = 2 x 2 x 2 x 11 x 11 x 11

= 2³ x 11³

³√10648 =   2×11=22

iv)  27000 = 2 x 2 x 2 x 3 x 3 x 3 x 5 x 5 x 5

= 2³ x 3³ x 5³

³√27000 =   2×3×5=30

v) 15625 = 5 x 5 x 5 x 5 x 5 x 5

= 5³x 5³

³15625 =   5×5=25

vi) 13824 = 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3

= 2³x 2³ x 2³ x 3³

³√13824 =   2×2×2×3=24

vii) 110592 = 2³ x 2³ x 2³ x 2³ x 3³

³√110592 =   2×2×2×2×3=48

viii) 46656 = 2 x 2 x 2 x 2 x 2 x 2 x 3 x 3 x 3 x 3 x 3 x 3

= 2³ x 2³ x 3³x 3³

³√46656 =   2×2×3×3=36

ix) 175616 = 2³x 2³ x 2³ x 7³

³√175616 =   2×2×2×7=56

x) 91125 = 5³ x 3³ x 3³

³√91125 =   5×3×3=45

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Hope this will help you...

thanks all my answera

Step-by-step explanation: