Answer:
81
Step-by-step explanation:
Let the digits that make up the number be a and b.
Given that the square root of the number is equal to the sum of the digits.
Then,
√(10a + b) = a + b
Also given that the square root of the number is less than the number obtained by interchanging the digits by 9, then
√(10a +b) + 9 = 10b + a
Since √(10a + b) = a + b, then
a + b + 9 = 10b + a
a - a + 9 = 10b - b
9b = 9
b = 1
since √(10a + b) = a + b
√(10a + 1) = a + 1
10a + 1= (a + 1)²
10a + 1 = a² + 2a + 1
a² + 2a - 10a + 1 - 1 = 0
a² - 8a = 0
a(a - 8) = 0
a = 0 or a = 8
Using a = 8 and b = 1,
the number 10a + b = 10(8) + 1 = 81.
