Identify the following as rational or irrational number. Give the decimal representation rational number.3 \sqrt{8}.

Foundation

Mathematics Foundation

Properties of Real Number

Irrational Number

Linear Equations in One Variable

Question

Identify the following as rational or irrational number. Give the decimal representation rational number.

3 \sqrt{8}

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First we will rewrite the given number,

\begin{aligned} 3 \sqrt{8} & a m p; = 3 \sqrt{4 \times 2} \\ a m p; = 3 \times 2 \sqrt{2} \\ a m p; = 6 \sqrt{2} \end{aligned}

\sqrt{2}

is irrational then

6 \sqrt{2}

3 \sqrt{8}

is irrational as well.

Now,

\begin{aligned} \sqrt{2}, & a m p; = 1.414213562 \\ a m p; \approx 1.41 \end{aligned}

So,

\begin{aligned} 3 \sqrt{8} & a m p;, = 6 \sqrt{2} \\ a m p; = 6 \times 1.41 \\ a m p; = 8.46 \end{aligned}