Question

The square of a two digit number is equal to that of a three digit number. The tens digit and the hundreds digit of the three digit number are equal. The units digit of the two-digit and the three digit numbers are equal. If the three-digit number exceeds 250, find its unit digit.

Answer 1

Answer:

5 is the unit digit.

Because the three digit number is the square of two digit number. The unit place of two digit and three digits are same. And the tenth digit and hundredth digit are same of the three digit number. There is only one with these conditions.

That is 15 and 225.

So when we add 225+250

We get 475.

Here the unit place is 5.

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Answer 2

Answer:

Required unit digit is 5.

Step-by-step explanation:

Here two digit number is 15 and three digit number is 225.

By opposite calculation we can prove this,

Given square of two digit number is equal to 3 digit number

Now ${15}^{2} = 225$

1St statement is satisfying.

Given tens digit and hundred digit are equal.

Here 3 digit number is 225.

Ten digit of 225 is 2 and hundred digit of 225 is also 2.

Second statement is satisfying.

Again given unit digit of two digit and three digit number are equal.

Here unit digit of 15 ans 225 are equal.

Third statement is satisfying.

So it is clear that two digit number is 15 and three digit number is 225.

Now The three-digit number exceeds 250.

So,$(225 + 250) = 475$

So, it's unit digit is 5.