Question

root 4/9 is irrational number

Answer 1

Concept

Irrational numbers are those numbers that cannot be expressed in terms of a fraction p/q where p and q both are non zero integers.

Given

A number $\sqrt{4/9}$ that is said to be irrational

Find

We have to check whether the given statement is true or false.

Solution

We have,

$\sqrt{4/9}$

here, square root of 4 is 2 and square root of 9 is 3

Therefore the number becomes-

$\sqrt{4/9}$ = 2/3

As we can see above 2/3 is not an rational number as it can be expressed as a fraction with non zero integer values.

Thus, the given statement that $\sqrt{4/9}$ is an irrational number is false.

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Answer 2

Answer:

The number $\sqrt{\frac{4}{9} }$ is not an irrational number.

Step-by-step explanation:

Irrational numbers: The numbers that cannot be written in the form of p/q, where p, q are integers and q ≠ 0.

Also, irrational numbers are non-terminating non- repeating decimals.

Step 1 of 1

Consider the given number as follows:

$\sqrt{\frac{4}{9} }$

Rewrite the given number as follows:

$\frac{\sqrt{4} }{\sqrt{9} }$ . . . . . (1)

The square root of $4$ is 2, i.e.,

$\sqrt{4} =2$

And the square root of $9$ is 3, i.e.,

$\sqrt{9} =3$

Then equation (1) becomes,

$\frac{\sqrt{4} }{\sqrt{9} }=\frac{2}{3}$

Observe that the number $\sqrt{\frac{4}{9} }$ can be written in the p/q form where 4, 9 are integers and also the denominator is non-zero.

Therefore, the number $\sqrt{\frac{4}{9} }$ is not an irrational number.

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