## 59th SSC CGL level Question Set, 3rd on topic fractions, square roots and surds

This is the 59th question set of 10 practice problem exercise for SSC CGL exam and 3rd on topic Fractions, square roots and surds. Students must complete this question set in prescribed time first and then only refer to the corresponding solution set for extracting maximum benefits from this resource.

In MCQ test, you need to deduce the answer in shortest possible time and select the right choice.

Based on our analysis and experience we have seen that, for accurate and quick answering, the student

- must have complete understanding of the basic concepts in the topic area
- is adequately fast in mental math calculation
- should try to solve each problem using the basic and rich concepts in the specific topic area and
- does most of the deductive reasoning and calculation in his or her head rather than on paper.

Actual problem solving is done in the fourth layer. You need to use **your problem solving abilities** to gain an edge in competition.

Before taking up the test you should refer to our concise tutorial on **Basic and rich concepts on Fractions decimals and surds part 1.**

### 59th question set- 10 problems for SSC CGL exam: 3rd on topic Fractions, square roots and surds - time 12 mins

**Problem 1.**

The value of $\sqrt{32}-\sqrt{128}+\sqrt{50}$ correct to 3 decimal places is,

- 1.441
- 1.732
- 1.414
- 1.141

**Problem 2.**

The square root of $\displaystyle\frac{\left(3\displaystyle\frac{1}{4}\right)^4-\left(4\displaystyle\frac{1}{3}\right)^4}{\left(3\displaystyle\frac{1}{4}\right)^2-\left(4\displaystyle\frac{1}{3}\right)^2}$ is,

- $1\displaystyle\frac{1}{12}$
- $1\displaystyle\frac{7}{12}$
- $7\displaystyle\frac{1}{12}$
- $5\displaystyle\frac{5}{12}$

**Problem 3.**

$\sqrt{11.981+7\sqrt{1.2996}}$ is closest to,

- 4.1
- 5.1
- 4.9
- 4.5

**Problem 4.**

The digit at the unit's place in the square root of 15876 is,

- 2
- 4
- 6
- 8

**Problem 5.**

The value of $120+3 \text{ of }5\div{\left[7\times{2}\left\{10\div{5}\left(24-10\times{2}+\overline{7+3\times{10}\div{5}}\right)\right\}\right]}$ is,

- 120.03
- 116.04
- 125
- 118

#### Problem 6.

Find the value of $\displaystyle\frac{1\displaystyle\frac{7}{9}\text{ of }\displaystyle\frac{27}{64}}{\displaystyle\frac{11}{12}\times{9\displaystyle\frac{9}{11}}}\div{\displaystyle\frac{4\displaystyle\frac{4}{7}\text{ of }\displaystyle\frac{21}{160}}{2\displaystyle\frac{5}{6}\div{2\displaystyle\frac{2}{15}}}}$.

- $\displaystyle\frac{421}{2443}$
- $\displaystyle\frac{425}{2434}$
- $\displaystyle\frac{425}{2344}$
- $\displaystyle\frac{425}{2304}$

** Problem 7.**

The value of $5\displaystyle\frac{1}{2}-\left[2\displaystyle\frac{1}{3}\div{\left\{\displaystyle\frac{3}{4}-\displaystyle\frac{1}{2}\left(\displaystyle\frac{2}{3}-\overline{\displaystyle\frac{1}{6}-\displaystyle\frac{1}{8}}\right)\right\}}\right]$ is,

- $\displaystyle\frac{1}{6}$
- $\displaystyle\frac{2}{3}$
- $\displaystyle\frac{1}{2}$
- $\displaystyle\frac{1}{4}$

** Problem 8.**

The smallest number that should be added to the number 8958 so that the result is a perfect square is,

- 67
- 69
- 79
- 77

**Problem 9.**

The largest number of 5 digits which is a perfect square is,

- 99999
- 99764
- 99976
- 99856

** Problem 10.**

The simplified value of $\displaystyle\frac{3\sqrt{2}}{\sqrt{3}+\sqrt{6}}-\displaystyle\frac{4\sqrt{3}}{\sqrt{6}+\sqrt{2}}+\displaystyle\frac{\sqrt{6}}{\sqrt{3}+\sqrt{2}}$ is,

- $\sqrt{2}$
- $\sqrt{3}-\sqrt{2}$
- $0$
- $\displaystyle\frac{1}{\sqrt{2}}$

For **answers and detailed solutions,** refer to the companion solution set to this question sets at **SSC CGL level Solution Set 59 on fractions decimals and surds 3.**