Join 60,000+ competitive exam aspirants
or with email
Your Cart
Subtotal₹0
Total₹0
Examoogle • User • info@examoogle.com • EE-2024-8821
Chapter 1 of 12 • Page 1 of 248🔒 Protected PDF • Watermarked
Join 60,000+ competitive exam aspirants
The sum of squares of two positive numbers is 145. If the square root of one of the numbers is 3, then find the other number.
9
136
8
64
8
Since the square root of the first number is 3, the number itself is 32=9. Subtracting its square (92=81) from the total sum (145) gives the square of the other number (145−81=64), which corresponds to 82.
Sum of squares of two positive numbers is 145. The square root of one number is 3.
x2+y2=145, x=3
Since the square root of the first number is 3, the number itself is 32=9. Subtracting its square (92=81) from the total sum (145) gives the square of the other number (145−81=64), which corresponds to 82.
Confusing the 'square root of a number' with the 'number' itself. Students often mistake the square root (3) for the number and subtract 32=9 from 145 instead of calculating the number first.
Identify the first number
Given that the square root of one of the numbers, let's call it x, is 3, we find x by squaring it.
x=32=9
Set up the equation for the second number
Let the two numbers be x and y. We are given x2+y2=145. We know x=9, so x2=81.
81+y2=145
Solve for the second number
Subtract 81 from both sides to find y2, then take the square root to find y.
y2=145−81=64⟹y=64=8
C is correct because the calculation 145−92=64 leads to 64=8.
This problem is a basic application of the Pythagorean theorem concept (a2+b2=c2). Identifying squares of numbers quickly (like 81 and 64) is essential for efficient mental calculation in competitive exams.
Get instant step-by-step AI explanations, full shift Previous Year Papers (SSC GD, RRB, SSC JE), and regional rank analysis on the official Examoogle App.
Free Download • 100K+ Aspirants