Question

Which of the following statements are true

Answer 1

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

Answer 2

Answer:

The correct statement is:

$\sqrt{\dfrac{5}{8}}$ is irrational and $\sqrt{\dfrac{4}{9}}$ is a rational number

Step-by-step 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:

$\sqrt{\dfrac{5}{8}}$ and $\sqrt{\dfrac{4}{9}}$

• Now we know that:

$\dfrac{5}{8}$ 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:

$\sqrt{\dfrac{5}{8}}=\dfrac{1}{2}\sqrt{\dfrac{5}{2}}$

( Since $8=2^3=2^2\times 2$)

• Whereas:

$\dfrac{4}{9}$ could also be written as:

$\dfrac{4}{9}=(\dfrac{2}{3})^2$

or

$\dfrac{4}{9}=(\dfrac{-2}{3})^2$

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

$\sqrt{\dfrac{4}{9}}=\pm \dfrac{2}{3}$

which is a rational number.