The sum of the squares of two odd numbers is 11570 . The square of the smaller number is 5329 . What is the other number? (a) 73 (b) 75 (c) 78 (d) 79 (e) None of these

Solution

Given the sum of the squares of two odd numbers is 11570, and the square of the smaller number is 5329, we can find the square of the other number as follows:

Step 1: Find the Square of the Other Number

The sum of the squares is given by:

\[
11570 = 5329 + x^2
\]

where \(x^2\) is the square of the other number. Solving for \(x^2\):

\[
x^2 = 11570 – 5329 = 6241
\]

Step 2: Determine the Other Number

To find the value of \(x\), we take the square root of 6241:

\[
x = \sqrt{6241} = 79
\]

Therefore, the other number is 79.

The correct answer is (d) 79.