Question

What is the square root of $169+25$ ?

Answer 1

Hint: In this question, we have to find the square root of an expression. Thus, we will use the basic mathematical rule and the LCM method to get the required solution. First, we will solve the addition of the given expression, after that we will put the square root sign in the answer. Then, we will find the LCM of the number and thus make the pair of two same terms. In the last, we will take a single number from the pairs and put it outside the square root, and the left non pair terms are put inside the square root, to get the required solution for the problem.

Complete step by step solution:
According to the problem, we have to find the square root of an expression.
Thus, we will use the basic mathematical rule and the LCM method to get the required solution.
The statement given to us is the square root of $169+25$ -------- (1)
So, now we will first do the addition of 169 and 25, we get
$\Rightarrow 169+25=194$
Thus, converting the statement (1) into mathematical statement, we get
$\sqrt{169+25}=\sqrt{194}$
Now, we will take the LCM of 194, that is
$\begin{align}
  & 02\left| \!{\underline {\,
 194 \,}} \right. \\
 & 97\left| \!{\underline {\,
 97 \,}} \right. \\
 & \text{ }\left| \!{\underline {\,
 1 \,}} \right. \\
\end{align}$
Thus, $LCM\left( 194 \right)=2\times 97$
Since, we cannot form a pair of the same terms from the above expression, thus we cannot simplify further.
Therefore, the square root of $169+25$ is equal to $\sqrt{194}$

Note: While solving this problem, do mention all the steps properly to avoid confusion and mathematical error. Do not write ‘the square root of $169+25$ ‘ as $\sqrt{169}+25$ , because it is not the correct way to show your solution. Also, do not split the square root with respect to addition, that is $\sqrt{169+25}\ne \sqrt{169}+\sqrt{25}$ , as it is the wrong interpretation.