# CBSE NCERT Solutions for Class 8 Chapter 7

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**CBSE NCERT Solutions for Class 8 Maths Chapter 7:**

*Question-1*:

Parikshit makes a cuboid of plasticine of sides 5cm, 2cm, 5cm. How many such cuboids will he need to form a cube?

*Solution*:

Given numbers = 5 x 2 x5

Since, Factors of 5 and 2 both are not in group of three.

Therefore, the number must be multiplied by 2 x 2 x 5 = 20 to make it a perfect cube.

Hence he needs 20cuboids.

*Question-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 with25.

(iv) There is no perfect cube which ends with8.

(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.

*Solution*:

(i) False

Since, 13= 1,33= 27,53= 125, ........................ are all odd.

(ii) True

Since, a perfect cube ends with three zeroes.

e.g. 103= 1000,203= 8000, 303= 27000, .................. so on

(iii) False

Since, 52= 25, 53= 125, 152= 225, 153 = 3375

( Did not end with 25)

(iv) False

Since 123= 1728 [Ends with 8]

And 223= 10648 [ Ends with 8 ]

(v) False

Since 103= 1000 [ Four digit number ]

And 113= 1331 [Four digit number]

(vi) False

Since 993= 970299 [ Six digit number ]

(vii)True

13= 1 [ Six digit number ]

23= 8 [ Six digit number]

*Question-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.

*Solution*:

(i) We know that 103= 1000 and Possible cube of 113= 1331

Since, cube of unitâ€™s digit 13 = 1

Therefore, cube root of 1331 is 11.

(ii) 4913

We know that 73=343

Next number comes with 7 as unit place 173 = 4913

Hence, cube root of 4913 is17.

(iii)12167

We know that 33=27

Here in cube, ones digit is7

Now next number with 3 as ones digit 133 = 2197

And next number with 3 as ones digit 233 = 12167

Hence cube root of 12167 is23.

(iv) 32768

We know that 23=8

Here in cube, ones digit is8

Now next number with 2 as ones digit 123 = 1728

And next number with 2 as ones digit 223 = 10648

And next number with 2 as ones digit 323 = 32768

Hence cube root of 32768 is32.