Question

Write true(T) or False(F) for the following statement-
No cube can end with exactly two zeroes.
A. True
B. False

Answer 1

Hint:
Cube number is the number which is multiplied by itself $3$ times. It is written in the exponential form ${a^3}$ where a represents the number being multiplied and the power represents the number of times it is multiplied. Since the number is multiplied three times the power is also three. Only square of a number having only its one’s digit as zero has exactly two zeroes.

Complete step by step solution:
We have to state whether it is true or not that No cube can end with exactly two zeroes.
Suppose we have to find the cube of a number with one zero say $10$
So ${10^3} = 10 \times 10 \times 10$
$ \Rightarrow {10^3} = 1000$ -- (i)
Now let’s find the cube of a number with two zeroes say $100$
So ${100^3} = 100 \times 100 \times 100$
$ \Rightarrow {100^3} = 1,000,000$
And as we go on increasing the number of zeroes we see that the cube of the numbers will have triple the number of zeroes compared to the original number.
So we see that if there is even one zero present in the number as the last digit then the cube of that number will have three zeroes.
So from eq. (i), it is not possible for the cube of a number having zero as its one’s digit to have less than three zeroes.
Hence it is true that No cube can have exactly two zeroes.

So the correct answer is A.

Note:
A square number is the number obtained when one number is multiplied by itself once to produce that square number. The numbers having only one zero as its one’s digit have exactly two zeroes.
For example- $10,20,130,480$ whose squares are $100,400,16900,230400$ respectively.
All these numbers have only one’s digit as zero and their squares have exactly two zeroes.