Question

What is the square root of $169$?

Answer 1

Hint: In this question we have been asked to find the square root of the number $169$, we will find the square root using the method of repeated subtraction. The repeated subtraction method states that we have to subtract successive odd numbers from the given number starting from $1$ onwards till we get the resultant as $0$. After getting $0$, the total number of times subtraction was done will give us the square root of the number.

Complete step-by-step solution:
We have the number given to us as:
$\Rightarrow 169$
Now we will use the repeated subtraction method and subtract odd numbers starting from $1$.
On subtracting $1$, we get:
$\Rightarrow 169-1=168$
On subtracting $3$, we get:
$\Rightarrow 168-3=165$
On subtracting $5$, we get:
$\Rightarrow 165-5=160$
On subtracting $7$, we get:
$\Rightarrow 160-7=153$
On subtracting $9$, we get:
$\Rightarrow 153-9=144$
On subtracting $11$, we get:
$\Rightarrow 144-11=133$
On subtracting $13$, we get:
$\Rightarrow 133-13=120$
On subtracting $15$, we get:
$\Rightarrow 120-15=105$
On subtracting $17$, we get:
$\Rightarrow 105-17=88$
On subtracting $19$, we get:
$\Rightarrow 88-19=69$
On subtracting $21$, we get:
$\Rightarrow 69-21=48$
On subtracting $23$, we get:
$\Rightarrow 48-23=25$
On subtracting $25$, we get:
$\Rightarrow 25-25=0$
Now in the last step we have got the value of subtraction as $0$which implies that we can write the square root of $0$.
Since we have used subtraction a total of $13$ time, the square root of $169=13$ therefore, it can be written as:
$\sqrt{169}=13$, which is the required solution.

Note: It is to be remembered that the repeated subtraction method should only be used for numbers that are small since it is a very lengthy method. If the value of the subtraction goes in negative then that number does not have a real root. It is also to be noted that the repeated subtraction method cannot be used for decimal numbers.