Answer:
Option 1 , 2 & 5
Step-by-step explanation:
4 & 16 are perfect squares. So , 1/4 & 1/16 are also perfect squares. But 2 , 8 & 10 are not perfect squares. So root of 1/2 , 1/8 & 1/10 are irrational numbers.
Verification :-
1)[tex] \sqrt{ \frac{1}{10} } = \frac{ \sqrt{1} }{ \sqrt{10} } = \frac{1}{ \sqrt{2} \times \sqrt{5} } [/tex]
Hence , it is irrational.
2)[tex] \sqrt{ \frac{1}{8} } = \frac{ \sqrt{1} }{ \sqrt{8} } = \frac{1}{2 \sqrt{2} } [/tex]
So , it is irrational.
3)[tex] \sqrt{ \frac{1}{16} } = \frac{ \sqrt{1} }{ \sqrt{16} } = \frac{1}{4} [/tex]
So , it is rational.
4) [tex] \sqrt{\frac{1}{4} } = \frac{ \sqrt{1} }{ \sqrt{4} } = \frac{1}{2} [/tex]
So it is rational.
5) [tex] \sqrt{ \frac{1}{2} } = \frac{ \sqrt{1} }{ \sqrt{2} } = \frac{1}{ \sqrt{2} } [/tex]
Hence it is irrational.
