Question

Which of the following statements are true

Answer 1

3rd that is it :( (hope this helps)

Answer 2

The correct statement is:

`\sqrt{(5)/(8)}` is irrational and
`\sqrt{(4)/(9)}` is a rational number

Explanation:

We know that if we get a non-square term under a square root sign than that term is considered to be an irrational number.

We are given two numbers:

`\sqrt{(5)/(8)}` and
`\sqrt{(4)/(9)}`

• Now we know that:

`(5)/(8)` is a non-square number.

Hence, on taking the square root of this number will give us a irrational number.

We can write it as:

`\sqrt{(5)/(8)}=(1)/(2)\sqrt{(5)/(2)}`

( Since
`8=2^3=2^2* 2`)

• Whereas:

`(4)/(9)` could also be written as:

`(4)/(9)=((2)/(3))^2`

or

`(4)/(9)=((-2)/(3))^2`

Hence, on taking square root of this number will give us:

`\sqrt{(4)/(9)}=\pm (2)/(3)`

which is a rational number.