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

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## Question

State True or False:

(i). Cube of any odd number is even.

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

(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 $$2$$-digit number may be a $$3$$-digit number.

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

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

## 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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