If the sum of the two-digit numbers formed from the digits a and b is a perfect square, the sum of the digits is

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If the sum of the two-digit numbers formed from the digits a and b is a perfect square, the sum of the digits is

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Answer 1

Given :- The sum of the two-digit numbers formed from the digits a and b is a perfect square.

Concept used :- 1. Calculate the sum of the digits for each of these two-digit numbers.

2. Check if any of these sums are perfect squares.

Solution :-

If a two-digit number is formed from the digits a and b, there are two possibilities: ab or ba, where a and b represent the tens and units place, respectively. The sum of these two numbers is given as a perfect square.

The number ab represents 10a + b, and the number ba represents 10b + a.

The sum of these two numbers then becomes (10a + b) + (10b + a), which simplifies to 11a + 11b, or 11 * (a + b).

So, for the sum of these two numbers to be a perfect square, the sum of the digits a and b (i.e., the value of "a + b") must be a divisor of a perfect square that is divisible by 11.

The smallest such number is 121 which is a perfect square of 11. And 121 is evenly divisible by 11.

So, the sum of the digits a and b would be 121 / 11 = 11.

Therefore, the correct option is 4) 11.

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If the sum of the two-digit numbers formed from the digits a and b is a perfect square, the sum of the digits is

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