NCERT Class 8 Mathematics Solutions: Chapter 7 – Cubes and Cube Roots Exercise 7.2 Part 3

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Image shows the cube and cube root of given number

Image Shows the Cube and Cube Root of Given Number

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 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.

Answer:

(i) Cube of any odd number is even.

e.g.

Cube of any odd number is odd not even.

So, this statement is false.

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

e.g.

Smallest two digit number is 10. hence, perfect cube does not ends with two zero but end with three or more zeroes.

So, this statement is true.

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

e.g. (Did not end with 25)

Square of a number ends with 5, but its cube does not ends with 25.

So, this statement is false.

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

e.g. [Ends with 8]

And [Ends with 8]

There are many perfect cube ends with 8.

So, this statement is false.

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

Since [Four digit number]

And [Four digit number]

Smallest two digit number is 10. Hence, cube of a two digit number is more than three digits.

So, this statement is false.

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

Since [Six digit number]

Biggest two digit number is 99. So, cube of a two digit number is less than seven digits.

So, this statement is false.

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

True

[Single digit number]

[Single digit number]

Here, cube of a single digit number may be a single digit number.

So, this statement is true.

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.

Answer:

We know that and

Possible cube of = 1331

Since, cube of unit’s digit

Therefore, cube root of 1331 is 11.

4913

We know that

Now, One’s place is 7 and ten’s place is

Hence, cube root of 4913 is 17.

12167

We know that

Here in cube, one’s digit is 7

Now, One’s place is 3 and ten’s place is

Next One’s place is 3 and ten’s place is

Hence cube root of 12167 is 23.

32768

We know that

Here in cube, one’s digit is 8

Now, One’s place is 2 and ten’s place is

Next One’s place is 2 and ten’s place is

Next One’s place is 2 and ten’s place is

Hence cube root of 32768 is 32.