Question

Determine whether the following number is rational, irrational, or not a real number. If the number is rational, give its exact value. If the number is irrational, give the decimal approximation to the nearest hundredth.

Answer 1

Irrational

Step-by-step explanation

We want to determine whether the number is rational, irrational, or not a real number.

A rational number is one that can be expressed as a fraction of two integers:

`(p)/(q)`

An irrational number is one that cannot be expressed as a fraction of two integers.

We are given the term:

`-√(1400)`

To do this, let us simplify the term:

`\begin{gathered} -√(1400)=-√(14*100) \\ \Rightarrow-√(14)*10 \\ \Rightarrow-10*√(14) \end{gathered}`

Since 14 is not a perfect square, its square root cannot be written as a fraction of two integers.

Let us simplify it:

`\begin{gathered} -10*3.742 \\ \Rightarrow-37.42 \end{gathered}`

Hence, it is an irrational number.