SSC CGL 2025 Tier-I · 21 September 2025, Shift 1 · Quantitative Aptitude · Question 5 of 99

We transcribed this text from the pictures on a candidate's response sheet for this shift; the answer is the key SSC colour-marked on that sheet. Solution last reviewed 13 September 2026.

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SSC does not publish CGL question papers or a public answer key. From 2025 the candidate response sheet prints every question and option as a picture, so the text here is transcribed from those pictures for this shift and checked against them independently; where the layout carries meaning, the picture is shown as well. Each answer is the key SSC colour-marked on that sheet. SSC released a tentative key for challenge and later its final one, both only to candidates behind a login, and the sheet does not say which of the two it carries. The solutions are written by UnlockIAS.

Which of the following is a perfect square and an Integer?

(a)Square root of 5
(b)Square root of 9
(c)3.2
(d)3.4

Answer

Why

Correct — B. Evaluate each option, then test it against the question.

√9 = 3, since 3² = 9
3 is a whole number, so √9 is an integer
It comes out whole because 9 is a perfect square

√5 ≈ 2.236, 3.2 and 3.4 each have a decimal part
So √9 is the option that is an integer → option (b)

Why the others are wrong

(a)
Square root of 5 — 5 is not a perfect square (2² = 4, 3² = 9), so √5 ≈ 2.236 is irrational and not an integer.
(c)
3.2 — 3.2 is not an integer: it lies between 3 and 4. A number with a decimal part cannot be an integer, so it fails the question at once.
(d)
3.4 — 3.4 is not an integer. It sits between 3 and 4, and a decimal part rules it out just as it rules out 3.2.

Concept

A perfect square is an integer that is the square of an integer: 1, 4, 9, 16, 25 …

The square root of a perfect square is an integer: √9 = 3, √16 = 4. The square root of any other positive integer is irrational, as √2, √5 and √7 are.

So √n, for a positive integer n, is an integer exactly when n is a perfect square.

Read strictly, the stem fits no option: √9 = 3 is an integer, but 3 itself is not a perfect square.

The question makes sense as "which option is the root of a perfect square, and so an integer". On that reading √9 is right, and none of the other options is even an integer.

Key facts

A perfect square is the square of an integer: 1, 4, 9, 16, 25, 36 …
For a positive integer n, √n is either an integer (when n is a perfect square) or irrational.
√5 ≈ 2.236, between 2 and 3.

Study next

Classifying numbers as natural, whole, integer, rational or irrationalWhether sums and products of surds are rationalUnit digits of perfect squares

Common traps

Calling 3 a perfect square because it came from √9. The perfect square is 9, and its root, 3, is the integer.
Assuming every square root is irrational. √9, √16 and √25 are whole numbers.

Number-type questions with short options also appear at 21 Sep 2025, 16:00, Quant Q.4 (real but not rational: keyed √7) and 20 Sep 2025, 12:30, Quant Q.8 (both integer and whole: keyed 0).

23 Sep 2025, 16:00, Quant Q.2 turns it round, asking for a number that is neither rational nor integer (keyed √2).

Related PYQs

No directly related past PYQ was found.

Topic: Square roots — all 48 SSC CGL questions on it, every solved shift.