Types and Simplest Form of Surds

Q.

Which of the following surds is/are pure surds?

1. $5-\sqrt{2}$

2. $\sqrt{3}$

3. $5\sqrt{2}$

4. $2+\sqrt{3}$

Q. Expressed 0.55.. in the form $\frac{p}{q}$ where p and q are integers and q ≠ 0.

Q. When you express $0$.$\overline{21}$ in the form $\frac{p}{q}$, where $p$ and $q$ are integers and $q\ne 0$, which of the following are the possible values of $(p+q)$?

1. 66
2. 72
3. 80
4. 96

Q. In the simplest $\frac{p}{q}$ form of $0.\overline{18}$, find p+q.

1. 13

Q. State which of the following are irrational numbers.
$(3–\sqrt{6}{)}^2$

Q.

Express the following mixed surd in the form of a pure surd.

$4\sqrt[3]{35}$

1. $\sqrt[3]{3320}$
2. $\sqrt[3]{3250}$
3. $\sqrt[3]{3625}$
4. $\sqrt[3]{31250}$

Q.

The value of $3\sqrt{54}÷2\sqrt{2}$ is

1. $\frac{2\sqrt{2}}{3}$

2. $\frac{9\sqrt{3}}{2}$

3. $\frac{\sqrt{3}}{2}$

4. $\frac{\sqrt{2}}{3}$

Q. In the simplest $\frac{p}{q}$ form of $0.\overline{18}$, find p+q.

1. 13

Q.

Which of the following is NOT a pair of like surds

1. $(2\times \sqrt[2]{263})$, $(3\times \sqrt[2]{212})$

2. $(7\times \sqrt[2]{2128})$, $(4\times \sqrt[2]{2242})$

3. $(5\times \sqrt[2]{2108})$, $(6\times \sqrt[2]{2192})$

4. $(3\times \sqrt[2]{280})$, $(4\times \sqrt[2]{2245})$

Q. State whether the given statement is true or false.
The sum of two irrational numbers is irrational.

1. True
2. False

Q.

Which one of the following is a compound surd?

1. $\sqrt[2]{212}+\sqrt[2]{227}+\sqrt[2]{248}$

2. $\sqrt[2]{248}+\sqrt[2]{280}+\sqrt[2]{220}$

3. 2$\times \sqrt[2]{272}+3\times \sqrt[2]{232}$

4. 5$\times \sqrt[2]{220}+2\times \sqrt[2]{245}+\sqrt[2]{280}$

Q. Burst the irrational numbers which can be expressed as the pure surds.

1. $\sqrt{5}$
2. $\sqrt{3}+\sqrt{2}$
3. $\sqrt{2}+\sqrt{8}$
4. $\sqrt[3]{354}$
5. $\sqrt[4]{44}$
6. \N
7. 3
8. $5\sqrt{2}$