Which number should be in the place of the question mark in the following? √ ? / 19= 4

Read the expression as √? ÷ 19 = 4. Multiply both sides by 19 to get √? = 76. Squaring both sides gives ? = 76², which is 5776. Check it: (75+1)² = 5625 + 150 + 1 = 5776. So the answer is C.

Why the others fail:

• A (5876): √5876 ≈ 76.66, and 76.66 ÷ 19 ≈ 4.03, not 4.
• B (5866): √5866 ≈ 76.58, giving about 4.03 after division. Not exact.
• D (5766): √5766 ≈ 75.93, and 75.93 ÷ 19 ≈ 3.996. Close to 4 but not exact.

The concept is reverse operation: undo the division, then undo the square root by squaring. This is the quantitative reasoning skill the aptitude paper tests, and it depends on speed and accuracy with perfect squares. The Mains link is thin, so treat it as a drill, not a topic.

Trap: aspirants estimate the root, see that 5766, 5866 and 5876 all sit near 76, and pick by feel. Always square the result exactly and compare.