Question

show that X is a rational number if X² =16/9​

Answer 1

Answer :-

$X {}^{2} = \frac{16}{9} \\ \\ X = \sqrt{ \frac{16}{9} } \\ \\ X = \frac{4}{3}$

4/3 can be represented in the form of p/q where q ≠ 0

so, 4/3 is a rational number

therefore, X is a rational number

__________________________

@MizzInnocenT

Answer 2

☯Given that x² = 16/9

☯We have to prove that x is rational number.

We know that rational number is basically the ratio of two numbers which can be written in the form of p/q where p and q are integers and q ≠ 0

So, to prove that x is a rational number, we have to solve given equation.

Solving:

x² = 16/9

→ x = $\sqrt{ \frac{16}{9} }$

→ x = $\frac{ \sqrt{16} }{ \sqrt{9} }$

(We know that √16 is equal to 4 and √9 is equal to 3)

→ x = 4/3

So, here we can see that x is equal to 4/3 which is in the form of p/q where p and q are integers and q≠0

Therefore,

☯ We can say that x is rational number •••$\large{\boxed{\bf{Proved}}}$