Question

1. Select all irrational numbers.

Answer 1

Answer: (1)$\sqrt{10}, \sqrt{27}, \sqrt{99}$, (2) $\sqrt{14}, \sqrt{24}, \sqrt{34}, \sqrt{44}, \sqrt{54}$, (3) $\sqrt{0.33}$ are irrational numbers.

Explanation:

(1)

A number is called an irrational number if it can not be written as a simple fraction form. For example $\sqrt{2}, \sqrt{3},\sqrt{5},...$.

If a real number is multiplied by an irrational number then the result is an irrational number.

$\sqrt{49}=7$

$\sqrt{64}=8$

Since the result of these square roots are a rational number, therefore $\sqrt{49}, \sqrt{64}$ these are rational numbers and $\sqrt{10}, \sqrt{27}, \sqrt{99}$ are irrational numbers.

(2)

$\sqrt{14} =\sqrt{7} \sqrt{2}$

$\sqrt{24} =2\sqrt{6}$

$\sqrt{14} =\sqrt{17} \sqrt{2}$

$\sqrt{44} =2\sqrt{11}$

$\sqrt{54} =3\sqrt{6}$

All the number in the option can not be written in the form of simple fraction, so all the options represents the irrational numbers.

(3)

$0.25=\frac{1}{4}$

$\sqrt{0.25} =0.5=\frac{1}{2}$

$\sqrt{0.33} =\frac{\sqrt{33}}{10}$

Therefore, the number $\sqrt{0.33}$ is an irrational number. The numbers $0.5,\sqrt{0.25}$ are rational numbers.

Answer 2

14√

24√ - Irrational 

34√ - Irrational 

44√ - Irrational 

54√ - Irrational