Question

How do you simplify the square root of 187 divided by the square root of 17?

Answer 1

Hint: In this question, we have to simplify the given mathematical term. Thus, we will apply the square root formula and then the basic mathematical rule, to get the solution. We start solving our problem, by using the square root formula in the fraction, that is $\dfrac{\sqrt{a}}{\sqrt{b}}=\sqrt{\dfrac{a}{b}}$ . After that, we will find the least common multiple of 187, which is equal to the product of 17 and 11. In the end, we will make the necessary calculations, to get the required solution for the problem.

Complete step by step solution:
According to the question, we have to simplify the given mathematical language.
Thus, we will use the square root formula and the basic mathematical rules to get the solution.
The mathematical language given to us is the square root of 187 divided by the square root of 17.
Thus, we can transform the above language into the mathematical terms as $\dfrac{\sqrt{187}}{\sqrt{17}}$ --- (1)
Now, we will apply the square root formula $\dfrac{\sqrt{a}}{\sqrt{b}}=\sqrt{\dfrac{a}{b}}$ in equation (1), we get
$\Rightarrow \sqrt{\dfrac{187}{17}}$ -------- (2)
Now, we will find the factors of 187 using factorization method, that is
$\begin{align}
  & 17\left| \!{\underline {\,
  187 \,}} \right. \\
 & 11\left| \!{\underline {\,
  11 \,}} \right. \\
 & \text{ }\left| \!{\underline {\,
  1 \,}} \right. \\
\end{align}$
Therefore, Factors(187)= $17\times 11$ ------- (3)
So, we will put the value of equation (3) in place of the numerator in equation (2), we get
$\Rightarrow \sqrt{\dfrac{17\times 11}{17}}$
As we know, the same terms in the numerator and the denominator cancel out each other as 1, we get
$\Rightarrow \sqrt{11}$ which is the required solution for the problem.

Therefore, the simplified value of the root of 187 divided by the square root of 17, is equal to $\sqrt{11}$.

Note: While solving this problem, do all the steps properly to avoid the mathematical errors. Do remember that the square root of a number implies the number has the power of the fraction, where the numerator is equal to 1 and the denominator is equal to 2, that is the power is equal to $\dfrac{1}{2}$ .