Ex.7.2 Q2 Cubes and Cube Roots - NCERT Maths Class 8

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Question

 State True or False:

Text Solution

(i). Cube of any odd number is even: 

Ans.  False

Reasoning:

Cubes of odd numbers are odd.

Cubes of even numbers are even.

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

Ans.  True

Reasoning:

Perfect cube may end with \(3\) zeros (or) groups of \(3\) zeros.

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

Ans.  False

Reasoning:

It is not always necessary that if the square of a number ends with \(5\), then its cube will end with \(25\).

For example, the square of \(5\) is \(25\) and \(25\) has its unit digit as \(5\). The cube of \(5\) is \(125\).

However, the square of \(15\) is \(225\) and also has its unit place digit as \(5\) but the cube of \(15\) is \(3375\) which does not end with \(25\).

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

Ans.  False

Reasoning:

The cubes of all the numbers having their unit place digit as \(2\) will end with \(8\).

The cube of \(12\) is \(1728\) and the cube of \(22\) is \(10648\).

(v). The cube of a \(2\)-digit number may be a \(3\)-digit number: 

Ans.  False

Reasoning:

Cube of a \(1\)-digit number may have \(1\)-digit to \(3\)-digits.

Cube of a \(2\)-digit number may have \(4\)-digits to maximum \(6\)-digits

(vi). The cube of a \(2\)-digit number may have seven or more digits: 

Ans.  False

Reasoning:

Cube of a \(1\)-digit number may have \(1\)-digit to \(3\)-digits.

Cube of a \(2\)-digit number may have \(4\)-digits to maximum \(6\)-digits.

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

Ans.  True

Reasoning:

Some examples

\[\begin{align}{1^3}&= 1\\{2^3}& = 8\end{align}\]

  
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