Cubes and Cube Roots Exercise 7.2

NCERT solutions for Class 8 Maths Cubes and Cube Roots 

NCERT Solutions for Class 8 Maths Cubes and Cube Roots

Class –VIII Mathematics (Ex. 7.2)

NCERT SOLUTION

1. Find the cube root of each of the following numbers by prime factorization method:

(i) 64    

(ii) 512

(iii) 10648    

(iv) 27000

(v) 15625    

(vi) 13824

(vii) 110592   

(viii) 46656

(ix) 175616   

(x) 91125

Ans. (i) 64

 =

= 4

(ii) 512

=   = 8

(iii) 10648

=

= 22

(iv) 27000

=

= 30

(v) 15625

=

= 25

(vi) 13824

=

= 24

(vii) 110592

=

= 48

(viii) 46656

 =

= 36

(ix) 175616

=

= 56

(x) 91125

= = 45

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NCERT Solutions for Class 8 Maths Exercise 7.2

2. State true or false:

(i) Cube of any odd number is even.

(ii) A perfect cube does not end with two zeroes.

(iii) If square of a number ends with 5, then its cube ends with 25.

(iv) There is no perfect cube which ends with 8.

(v) The cube of a two digit number may be a three digit number.

(vi) The cube of a two digit number may have seven or more digits.

(vii) The cube of a single digit number may be a single digit number.

Ans. (i) False

Since,  are all odd.

(ii) True

Since, a perfect cube ends with three zeroes. e.g. so on

(iii) False

Since,

(Did not end with 25)

(iv) False

Since   = 1728

[Ends with 8]

And  = 10648

[Ends with 8]

(v) False Since  = 1000

[Four digit number]

And  = 1331

[Four digit number]

(vi) False Since  = 970299

[Six digit number]

(vii) True

 = 1

[Single digit number]

 = 8

[Single digit number]

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NCERT Solutions for Class 8 Maths Exercise 7.2

3. You are told that 1,331 is a perfect cube. Can you guess with factorization what is its cube root? Similarly guess the cube roots of 4913, 12167, 32768.

Ans. We know that  = 1000 and Possible cube of  = 1331

Since, cube of unit’s digit  = 1

Therefore, cube root of 1331 is 11.

4913

We know that  = 343

Next number comes with 7 as unit place  = 4913

Hence, cube root of 4913 is 17.

12167

We know that  = 27

Here in cube, ones digit is 7

Now next number with 3 as ones digit

 = 2197

And next number with 3 as ones digit

 = 12167

Hence cube root of 12167 is 23.

32768

We know that  = 8

Here in cube, ones digit is 8

Now next number with 2 as ones digit

 = 1728

And next number with 2 as ones digit

 = 10648

And next number with 2 as ones digit

 = 32768

Hence cube root of 32768 is 32.

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