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SSC CHSL 13 Nov 2025 Shift 3 Paper

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Question : 65 of 100

Marks: +1, -0

What is the value of the expression

\sqrt{(12345)^{2}+12345+12346}

?

12345
12346
12347
12344

Solution:

Concept:

The expression inside the square root can be rewritten as a perfect square using the identity

(a+1)^2 = a^2 + 2a + 1

.

Explanation:

First, rewrite

12346

as

12345 + 1

.

Then the expression becomes

\sqrt{(12345)^2 + 12345 + (12345 + 1)}

.

Combine terms:

\sqrt{(12345)^2 + 2 \times 12345 + 1}

.

This matches the form

a^2 + 2a + 1

with

a = 12345

, so it equals

(12345 + 1)^2 = (12346)^2

.

Finally,

\sqrt{(12346)^2} = 12346

.

Answer:

12346

(Option B)

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