Question

What is the value of $\sqrt{196}÷\sqrt{144}?$

• A. $\frac{7}{12}$
  
• B. $\frac{14}{6}$
  
• C. $\frac{7}{6}$
  
• D. None of the above

Answer 1

The correct option is C $\frac{7}{6}$


First, we would find the square root of $196$ using long division method.

$\sqrt{196}$ using long division method can be evaluated as:


$\therefore \underset{–}{\sqrt{196}=14}$

Now, we would find the square root of $144$ using long division method.


$\therefore \underset{–}{\sqrt{144}=12}$

Now,
$\sqrt{196}÷\sqrt{144}=\frac{\sqrt{196}}{\sqrt{144}}$

$\Rightarrow \sqrt{196}÷\sqrt{144}=\frac{14}{12}$

$\Rightarrow \sqrt{196}÷\sqrt{144}=\frac{2\times 7}{2\times 6}$

$\Rightarrow \underset{–}{\sqrt{196}÷\sqrt{144}=\frac{7}{6}}$

As a result, the value of $\sqrt{196}÷\sqrt{144}$ is $\frac{7}{6}$.

Therefore, option (c.) is the correct answer.