Question

Simplify the given value \[\sqrt {169} \times \sqrt {361} \]

Answer 1

Hint: According to the question, solve the \[\sqrt {169} \] and \[\sqrt {361} \] separately. Then, put the calculated values in the given question to get the desired result.


Complete step-by-step answer:
As it is given \[\sqrt {169} \times \sqrt {361} \] we have to simplify it.
We will proceed this equation \[\sqrt {169} \times \sqrt {361} \] step by step.
Firstly, we will calculate square root of 169 that is \[\sqrt {169} \]
We will solve, 169 with the help of factorisation we can calculate it.
Here, we will solve until dividing we get remainder 0 and quotient at end is 1.
As, 169 is only divisible with 13 so we get remainder 0 and quotient 13 that is \[\dfrac{{169}}{{13}} = 13\] Now, again dividing quotient as the quotient is not equal to 1.
So, 13 is divisible by 13 only so we get remainder 0 and quotient 1 that is \[\dfrac{{13}}{{13}} = 1\].
As, the quotient is equal to 1. So, we did not solve it further.
Hence, factors of 169 come out to be \[13 \times 13\] .
So, \[\sqrt {169} \] is 13 because the digit appearing two times is considered as one time while calculating square root.
Secondly, we will calculate square root of 361 that is \[\sqrt {361} \]
We will solve 361 with the help of factorisation we can calculate it.
Here, we will solve until dividing we get remainder 0 and quotient at end is 1.
As, 361 is only divisible with 19 so we get remainder 0 and quotient 19 that is \[\dfrac{{361}}{{19}} = 19\] Now, again dividing quotient as the quotient is not equal to 1.
So, 19 is divisible by 19 only so we get remainder 0 and quotient 1 that is \[\dfrac{{19}}{{19}} = 1\].
So, we did not solve it further.
Hence, factors of 361 come out to be \[19 \times 19\] .
So, \[\sqrt {361} \] is 19 because the digit appearing two times is considered as one time while calculating square root.
Putting the values of \[\sqrt {169} \] and \[\sqrt {361} \] in the given equation we get,
\[ \Rightarrow 13 \times 19\]
\[ \Rightarrow 247\]
So, \[\sqrt {169} \times \sqrt {361} \]\[ \Rightarrow 247\]


Note: In these types of questions, we first solve the square roots of the given numbers. Then, proceed according to the question and do the simplification as required for the calculation of the result.