Sum of squares of two numbers is 145. If square root of one number is 3, the other number is equal to :

Question

Accepted Answer

To solve the problem, we need to determine the value of the other number given that the sum of the squares of two numbers is 145 and the square root of one number is 3.

1. **Understanding the Problem:**
   - Let the two numbers be $ x $ and $ y $.
   - We know that the square root of one number is 3. Therefore, the number itself is $ 3^2 = 9 $.
   - The sum of the squares of the two numbers is given as 145. Therefore, we have the equation:
     $$
     9^2 + y^2 = 145
     $$

2. **Solving the Equation:**
   - Calculate $ 9^2 $:
     $$
     9^2 = 81
     $$
   - Substitute this into the equation:
     $$
     81 + y^2 = 145
     $$
   - Solve for $ y^2 $:
     $$
     y^2 = 145 - 81 = 64
     $$
   - Find $ y $ by taking the square root of 64:
     $$
     y = \sqrt{64} = 8
     $$

3. **Conclusion:**
   - Therefore, the other number is 8, which corresponds to Option 4.

4. **Explanation of Incorrect Options:**
   - **Option 1 (136):** If the other number were 136, then $ 136^2 $ would be a very large number, far exceeding 145 when added to $ 9^2 $.
   - **Option 2 (64):** If the other number were 64, then $ 64^2 $ would also be a very large number, far exceeding 145 when added to $ 9^2 $.
   - **Option 3 (9):** If the other number were 9, then the sum of the squares would be $ 9^2 + 9^2 = 81 + 81 = 162 $, which is greater than 145.

Thus, the only correct and feasible solution is Option 4, where the other number is 8.