## Surds and Indices Questions Set 7 and 73rd for SSC CGL

Surds and indices questions for SSC CGL in this 7th set have a number of difficult questions. Use Surds problem solving techniques to solve the questions.

This 73rd question set for SSC CGL may be used for any competitive exam.

Take the timed test and score your performance from the answers at the end.

If you need, clear your doubts from the solutions. Link given at the end.

### Recommended reading before the test

The articles below cover almost all the Surds problem solving techniques in details. Do go through before or after taking the test.

**How to solve surds part 1 - Rationalization of surds.**

**How to solve surds part 2 - Double square root surds and surd term factoring.**

**How to solve surds part 3 - Surds expression comparison and ranking.**

**How to solve difficult surd algebra problems in a few simple steps 4.**

For *gaining complete grip on surds and indices questions*, use our **Surds and indices guide** with links on all tutorials, questions sets and solution sets on surds and indices.

Best way to use this surds and indices question set is to *first practice on a few earlier question sets on the topic* and **then take this test with timer on.**

### 7th Set of Surds and Indices Questions 73rd for SSC CGL - answering time 15 mins

#### Problem 1.

The value of $\displaystyle\frac{3\sqrt{2}-2\sqrt{3}}{3\sqrt{2}+2\sqrt{3}}+\displaystyle\frac{\sqrt{12}}{\sqrt{3}-\sqrt{2}}$ is,

- $11$
- $-12$
- $12$
- $-11$

#### Problem 2.

Value of $\displaystyle\frac{\sqrt{5}+\sqrt{3}}{\sqrt{80}+\sqrt{48}-\sqrt{45}-\sqrt{27}}$ is,

- $-2$
- $-1$
- $2$
- $1$

#### Problem 3.

Simplify $\displaystyle\frac{6}{2\sqrt{3}-\sqrt{6}}+\displaystyle\frac{\sqrt{6}}{\sqrt{3}+\sqrt{2}}-\displaystyle\frac{4\sqrt{3}}{\sqrt{6}-\sqrt{2}}$ is,

- $1$
- $2$
- $0$
- $-1$

#### Problem** 4.**

Simplify $\displaystyle\frac{4\sqrt{18}}{\sqrt{12}}-\displaystyle\frac{8\sqrt{75}}{\sqrt{32}}+\displaystyle\frac{9\sqrt{2}}{\sqrt{3}}$.

- $2$
- $0$
- $-1$
- $1$

#### Problem** 5.**

Value of

$\displaystyle\frac{1}{1+\sqrt{2}}+\displaystyle\frac{1}{\sqrt{2}+\sqrt{3}}+\displaystyle\frac{1}{\sqrt{3}+\sqrt{4}}$

$+\displaystyle\frac{1}{\sqrt{4}+\sqrt{5}}+\displaystyle\frac{1}{\sqrt{5}+\sqrt{6}}+\displaystyle\frac{1}{\sqrt{6}+\sqrt{7}}$

$+\displaystyle\frac{1}{\sqrt{7}+\sqrt{8}}+\displaystyle\frac{1}{\sqrt{8}+\sqrt{9}}$ is,

- $0$
- $-2$
- $2$
- $1$

#### Problem 6.

If $a=\displaystyle\frac{1}{3+2\sqrt{2}}$ and $b=\displaystyle\frac{1}{3-2\sqrt{2}}$, the value of $a^2b +ab^2$ is,

- $-5$
- $6$
- $-6$
- $5$

#### Problem** 7.**

If $x=\displaystyle\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}$ and $y=\displaystyle\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}$, the value of $x^3+y^3$ is,

- 807
- 907
- 870
- 970

#### Problem** 8.**

If $x=\sqrt{\displaystyle\frac{5+2\sqrt{6}}{5-2\sqrt{6}}}$ find the value of $x^2(x-10)^2$,

- $-1$
- $-2$
- $1$
- $2$

#### Problem** 9.**

Arrange $3^{34}$, $2^{51}$, and $7^{17}$ in decending order of decreasing values,

- $3^{34}$ > $2^{51}$ > $7^{17}$
- $2^{51}$ > $3^{34}$ > $7^{17}$
- $3^{34}$ > $7^{17}$ > $2^{51}$
- $7^{17}$ > $2^{51}$ > $3^{34}$

#### Problem** 10.**

$4^{61}+4^{62}+4^{63}+4^{64}$ is divisible by,

- $3$
- $11$
- $13$
- $17$

To clear your doubts and know how to solve these questions quickly with confidence, our solutions should a be a great help to you. Below is the link.

**SSC CGL Solution Set 73 Surds and Indices 7.**

### Answers to the questions

**Problem 1.** Answer: Option a: $11$.

**Problem 2.** Answer. Option d: $1$.

**Problem 3.** Answer: Option c: $0$.

**Problem 4.** Answer: Option b: $0$.

**Problem 5.** Answer: Option c: $2$.

**Problem 6.** Answer: Option b: $6$.

**Problem 7.** Answer: Option d: 970.

**Problem 8.** Answer: Option c: 1.

**Problem 9.** Answer. Option a: $3^{34}$ > $2^{51}$ > $7^{17}$.

**Problem 10.** Answer: Option d: 17.

### Guided help on Fractions, Surds and Indices in Suresolv

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