Question

Find the value of the given expression using prime factorization.

$\frac{\sqrt{169}}{12}\times \frac{19}{14}\times \frac{\sqrt{196}}{13}$

• A. $\frac{7}{12}$
• B. $1\frac{7}{12}$

Answer 1

The correct option is B $1\frac{7}{12}$

Let's find the square root of $169$ and $196.$

Prime factorization of $169$ and $196$ are as follows:
$169=13\times 13$
$\Rightarrow 169={13}^2$

$196=2\times 2\times 7\times 7$
$\Rightarrow 196=(2\times 7)\times (2\times 7)$
$\Rightarrow 196=(14{)}^2$

$\therefore \frac{\sqrt{169}}{12}\times \frac{19}{14}\times \frac{\sqrt{196}}{13}=\frac{13}{12}\times \frac{19}{14}\times \frac{14}{13}$
(canceling the common terms)
$=\frac{19}{12}$
$=\frac{12+7}{12}$
​​​​​​​$=1+\frac{7}{12}$
​​​​​​​$=1\frac{7}{12}$