Question

examine √13/117 is a rational nomber

Answer 1

Step-by-step explanation:

To examine

$\sqrt{ \frac{13}{117} }$

is a rational number or not.

Step 1: Do prime factors of 117

$117 = 3 \times 3 \times 13$

Step2: Place these factors

$\sqrt{ \frac{13}{3 \times 3 \times 13} } \\ \\ = > \sqrt{ \frac{1}{ {(3)}^{2} } } \\ \\ = > \frac{1}{3}$

here we can see that

$\sqrt{ \frac{13}{117} } = \frac{1}{3}$

Thus it can be expressed as P/Q,where P and Q are integers and Q≠0.

So ,it is a rational number.

Hope it helps you.

Answer 2

Answer:

rational

Step-by-step explanation:

To examine

\sqrt{ \frac{13}{117} }

117

13

is a rational number or not.

Step 1: Do prime factors of 117

\begin{gathered}117 = 3 \times 3 \times 13 \\ \\ \end{gathered}

117=3×3×13

Step2: Place these factors

\begin{gathered} \sqrt{ \frac{13}{3 \times 3 \times 13} } \\ \\ = > \sqrt{ \frac{1}{ {(3)}^{2} } } \\ \\ = > \frac{1}{3} \\ \\ \end{gathered}

3×3×13

13

=>

(3)

2

1

=>

3

1

here we can see that

\begin{gathered} \sqrt{ \frac{13}{117} } = \frac{1}{3} \\ \\ \end{gathered}

117

13

=

3

1

Thus it can be expressed as P/Q,where P and Q are integers and Q≠0.

So ,it is a rational number.

Hope it helps you.