Introduction to Irrational Numbers

Q. Find the hypotenuse of a right angled triangle whose perpendicular sides are $\sqrt{6}$ cm and $\sqrt{3}$ cm.

Q.

For which of the following numbers is the square root a rational number?

1. 7.29

2. 2.5

3. 0.4

4. 13

Q.

Rational numbers are a subset of ___ .

1. whole numbers

2. natural numbers

3. real numbers

4. integers

Q.

If 14.287628762876........ can be represented in $\frac{p}{q}$ form, then 'p - q ' is ________.

1. 142862

2. 142876

3. 142863

4. 132863

Q.

Which one of the following numbers is a non-terminating and repeating decimal?

1. $\frac{39}{24}$

2. $\frac{3}{11}$

3. $\frac{49}{56}$

4. $\frac{78}{32}$

Q.

Numbers whose decimal representation is non terminating and non repeating is a/an _________.

1. fraction

2. irrational number

3. rational number

4. integer

Q.

An irrational number between $\frac{1}{7}$ and $\frac{2}{7}$ is

1. $(\frac{1}{7}+\frac{2}{7})$

2. $\frac{1}{2}(\frac{1}{7}+\frac{2}{7})$

3. $\sqrt{\frac{1}{7}\times \frac{2}{7}}$

4. None of these

Q.

The number $1.\overline{27}$ in the form $\frac{p}{q}$, where p and q are integers and q $\ne$ 0, is

1. $\frac{14}{11}$

2. $\frac{14}{9}$

3. $\frac{14}{13}$

4. $\frac{14}{15}$

Q.

How do we represent $0.123\overline{456}$?

1. $\frac{41111}{999000}$

2. $\frac{41111}{333000}$

3. $\frac{3333}{99000}$

4. $\frac{12333}{99000}$

Q.

If x = 2z, then x is ________

1. An odd number

2. special number

3. prime number

4. An even number