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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.

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 gi class=


Answer :

ANSWER

Irrational

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:

[tex]\frac{p}{q}[/tex]

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

We are given the term:

[tex]-\sqrt{1400}[/tex]

To do this, let us simplify the term:

[tex]\begin{gathered} -\sqrt{1400}=-\sqrt{14*100} \\ \Rightarrow-\sqrt{14}*10 \\ \Rightarrow-10*\sqrt{14} \end{gathered}[/tex]

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

Let us simplify it:

[tex]\begin{gathered} -10*3.742 \\ \Rightarrow-37.42 \end{gathered}[/tex]

Hence, it is an irrational number.

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