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SSC MTS 9 Feb 2026 Shift 3 Paper

Question : 12 of 150

Marks: +1, -0

\frac{\sqrt{8}+\sqrt{50}}{\sqrt{18}}=?

Solution:

Concept:

Simplify each radical by extracting perfect squares, then combine like surds.

Explanation:

Rewrite each square root as a product of a perfect square and a remaining factor.

\sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2}

\sqrt{50} = \sqrt{25 \times 2} = 5\sqrt{2}

\sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2}

Now substitute into the expression:

(2\sqrt{2} + 5\sqrt{2}) \div (3\sqrt{2})

Add the like surds in the numerator:

(2 + 5)\sqrt{2} = 7\sqrt{2}

The expression becomes

\frac{7\sqrt{2}}{3\sqrt{2}} = \frac{7}{3}

(the

\sqrt{2}

cancels out).

Answer:

\frac{7}{3}

, which corresponds to option C.

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