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SSC MTS 5 Feb 2026 Shift 3 Paper

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Question : 18 of 150

Marks: +1, -0

\sqrt{10.89}+\sqrt{0.1089}+\sqrt{0.001089}+\sqrt{0.00001089}+\sqrt{0.0000001089}=?

3.66665
3.6663
3.66663
3.6661

Solution:

Concept:

Each number is a perfect square of the form

\frac{1089}{10^{2k}}

. Its square root is

\frac{33}{10^k}

, allowing direct decimal placement.

Explanation:

Since

\sqrt{1089}=33

, rewrite each term:

\sqrt{10.89} = \sqrt{\frac{1089}{100}} = \frac{33}{10}=3.3

\sqrt{0.1089} = \sqrt{\frac{1089}{10000}} = \frac{33}{100}=0.33

\sqrt{0.001089} = \sqrt{\frac{1089}{1000000}} = \frac{33}{1000}=0.033

\sqrt{0.00001089} = \sqrt{\frac{1089}{100000000}} = \frac{33}{10000}=0.0033

\sqrt{0.0000001089} = \sqrt{\frac{1089}{10000000000}} = \frac{33}{100000}=0.00033

Now add them in order:

3.3 + 0.33 = 3.63

3.63 + 0.033 = 3.663

3.663 + 0.0033 = 3.6663

3.6663 + 0.00033 = 3.66663

Answer:

3.66663

(Option C)

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