Question

Fill in the blanks:
When a square number _________ is 6, the number whose square it is, will have either 4 or 6 in the _________ place.
(a) ends, units
(b) starts, units
(c) ends, tens
 (d) starts, tens

Answer 1

Hint: Here, we need to fill the blanks using the correct option. We will use the concept of square and square roots to determine which option is true, to find the correct option. We will also use some examples to check if the answer is correct or not.

Complete step-by-step answer:
We will use square and square roots to determine which is true, to find the correct option.
The number whose square the square number is, is called the square root.
For example: 9 is the square of 3. Thus, we can say that 3 is the square root of 9.
Let us find the squares of some numbers that have 4 or 6 in the ten’s place.
The square of 41 is 1681.
The square of 48 is 2304.
The square of 63 is 3969.
The square of 69 is 4761.
We can observe that if the number has either 4 or 6 in the ten’s place, then it is not necessary that its square has 6 in either the start or the end.
Thus, option (c) and option (d) are incorrect.
Now, we will find the squares of some numbers that have 4 or 6 in the unit’s place.
The square of 24 is 576.
The square of 46 is 2116.
The square of 74 is 5476.
The square of 96 is 9216.
We can observe that if the number has either 4 or 6 in the unit’s place, then its square always has the digit 6 in the end.
Therefore, when a square number ends in 6, the number whose square it is, will have either 4 or 6 in the units place.
Thus, the correct option is option (a).

Note: Let us also check the option (b).
We found the squares of some numbers that have 4 or 6 in the unit’s place.
The square of 24 is 576.
The square of 46 is 2116.
The square of 74 is 5476.
The square of 96 is 9216.
We can observe that if the number has either 4 or 6 in the unit’s place, then it is not necessary that its square has 6 in the start.
Thus, option (b) is incorrect.