Question

Explain why the square root of 38 is an irrational number.

Pls help me.

Answer 1

The number
`√(38)` is an irrational number as the decimal expansion of numbers is neither terminate nor periodic.

Explanation:

Consider the provided number.

`√(38)`

Irrational number: A number is irrational if it cannot be expressed be expressed by dividing two integers. The decimal expansion of Irrational numbers are neither terminate nor periodic.

The value of the provided number in decimal form is:

`√(38)=6.164414..`

The number
`√(38)` is an irrational number as the decimal expansion of numbers is neither terminate nor periodic.

Answer 2

For this case we have that by definition, an irrational number is one that cannot be expressed as the exact ratio of two integers
`\frac {a} {b}`, where b is different from 0.

We have to:

`\sqrt {38} = 6.164414002968`

Obviously, this number meets the definition given. Thus, it is an irrational number.

ANswer:

It is an irrational number.