SSC CGL 2025 Tier-I · 14 September 2025, Shift 3 · Quantitative Aptitude · Question 23 of 95

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.

Where this paper and its answers come from

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.

Simplify: √50 + √18 − √8

(a)7√2
(b)6√2
(c)5√2
(d)8√2

Answer

Why

Correct — B.
Method: write each root as a whole number × √2 by pulling out the largest perfect square.

√50 = √(25 × 2) = 5√2
√18 = √(9 × 2) = 3√2
√8 = √(4 × 2) = 2√2

Combine the like surds: 5√2 + 3√2 − 2√2 = (5 + 3 − 2)√2 = 6√2 → option (b)

Why the others are wrong

(a)
7√2 — 7√2 would need √8 = √2, a subtraction of just 1√2. But √8 = √(4 × 2) = 2√2, so the total is 5 + 3 − 2 = 6 lots of √2.
(c)
5√2 — 5√2 is √50 alone. The other two terms do not cancel: √18 − √8 = 3√2 − 2√2 = √2, which lifts the total to 6√2.
(d)
8√2 — 8√2 is √50 + √18 = 5√2 + 3√2 with the − √8 left out. Subtracting 2√2 brings it down to 6√2.

Concept

Surds combine only when the number under the root matches: 5√2 + 3√2 = 8√2, just as 5x + 3x = 8x.

So first simplify each root with √(a × b) = √a × √b, taking a as the largest perfect-square factor.

Here 50, 18 and 8 are 25 × 2, 9 × 2 and 4 × 2, so all three become multiples of √2 and the coefficients add and subtract like ordinary numbers.

The four options are all multiples of √2 and differ by one step each, so a single slip in one root (2√2 read as √2 or 3√2) lands on a printed option.

Key facts

√(a × b) = √a × √b for non-negative a and b.
√50 = 5√2, √18 = 3√2 and √8 = 2√2.
Like surds, with the same number under the root, combine by adding their coefficients.

Study next

Simplifying surds with √3 and √5 factors, such as √75 = 5√3 and √45 = 3√5Squaring a surd sum: (√a + √b)² = a + b + 2√(ab)Rationalising with a conjugate, such as 1⁄(√3 − √2) = √3 + √2

Common traps

Adding under one root: √50 + √18 − √8 is not √(50 + 18 − 8) = √60.
Dropping the minus term and stopping at 5√2 + 3√2 = 8√2.

This stem strings three roots that all reduce to multiples of √2. The same four options (7√2, 6√2, 5√2, 8√2) appear at 15 Sep 2025, 12:30, Quant Q.21, where √98 − √32 + √50 = 7√2 − 4√2 + 5√2 is keyed 8√2, so a remembered answer does not carry over.

Related PYQs

No directly related past PYQ was found.

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