Question

Select all irrational numbers.

Answer 1

Option 1 , 2 & 5

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)
`\sqrt{ (1)/(10) } = ( √(1) )/( √(10) ) = (1)/( √(2) * √(5) )`

Hence , it is irrational.

2)
`\sqrt{ (1)/(8) } = ( √(1) )/( √(8) ) = (1)/(2 √(2) )`

So , it is irrational.

3)
`\sqrt{ (1)/(16) } = ( √(1) )/( √(16) ) = (1)/(4)`

So , it is rational.

4)
`\sqrt{(1)/(4) } = ( √(1) )/( √(4) ) = (1)/(2)`

So it is rational.

5)
`\sqrt{ (1)/(2) } = ( √(1) )/( √(2) ) = (1)/( √(2) )`

Hence it is irrational.

Answer 2

Square root of 1/10and 1/8 and 1/2 are the only irrational numbers