Answer: (1)[tex]\sqrt{10}, \sqrt{27}, \sqrt{99}[/tex], (2) [tex]\sqrt{14}, \sqrt{24}, \sqrt{34}, \sqrt{44}, \sqrt{54}[/tex], (3) [tex]\sqrt{0.33}[/tex] 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 [tex]\sqrt{2}, \sqrt{3},\sqrt{5},...[/tex].
If a real number is multiplied by an irrational number then the result is an irrational number.
[tex]\sqrt{49}=7[/tex]
[tex]\sqrt{64}=8[/tex]
Since the result of these square roots are a rational number, therefore [tex]\sqrt{49}, \sqrt{64}[/tex] these are rational numbers and [tex]\sqrt{10}, \sqrt{27}, \sqrt{99}[/tex] are irrational numbers.
(2)
[tex]\sqrt{14} =\sqrt{7} \sqrt{2}[/tex]
[tex]\sqrt{24} =2\sqrt{6}[/tex]
[tex]\sqrt{14} =\sqrt{17} \sqrt{2}[/tex]
[tex]\sqrt{44} =2\sqrt{11}[/tex]
[tex]\sqrt{54} =3\sqrt{6}[/tex]
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)
[tex]0.25=\frac{1}{4}[/tex]
[tex]\sqrt{0.25} =0.5=\frac{1}{2}[/tex]
[tex]\sqrt{0.33} =\frac{\sqrt{33}}{10}[/tex]
Therefore, the number [tex]\sqrt{0.33}[/tex] is an irrational number. The numbers [tex]0.5,\sqrt{0.25}[/tex] are rational numbers.
