Question

Subtracting which odd number will get the value of $288$ for square root of the number $484$ using repeated subtraction method?

Answer 1

Hint: We are given a number $484$, we are asked to find the odd number which will be subtracted to get $288$, to do so we will first learn about the repeated subtraction method, then we will learn some examples to get a grip then at last we will start our problem, we will start subtracting odd numbers from $1-484$ till we get $288$.

Complete step by step solution:
We are given that while finding the square root of $484$ using repeated subtraction method we get $288$ in between, we have to find the odd numbers which are subtracted to get $288$. To do this we start by learning about the odd number, the repeated subtraction method of square root.
Now, odd numbers are those natural numbers which are not divisible by $2$ like, $3,5$. Odd numbers start from $1$. So, $1,3,5,7,9$ etc are all odd numbers. Now, the repeated subtraction method is a technique of finding square roots in which we subtract succession odd numbers from $1\,to\,121$.
The number of steps obtained to get the result $0$ is the square root of the given number.
For example, consider if, we will find the square root of $16$
We start by subtracting odd number from $16$
$\Rightarrow 16-1=15$ (as first odd number is $1$)
Next odd number is $3$,
$\Rightarrow 15-3=12$
Third odd number is $5$
$\Rightarrow 12-5=7$
Next odd number is $7$
$7-7=0$
So in $4$ steps we get $0$, So $4$ is square root of $16$.
Now if we say look for odd numbers which will get the value $12$
So we can see that when $3$ is subtracted, it gives $12$
$3$ is the one we worked for.
Now to find the number which when subtracted gives, we will use this method.
So we start subtracting odd numbers from $484$ start with $1$ and go on with, $3,5,7,9,11,13,15$
$\begin{align}
  & 484-1=483 \\
 & 483-3=480 \\
 & 480-5=475 \\
 & 475-7=468 \\
 & 468-9=459 \\
 & 459-11=448 \\
 & 448-13=435 \\
\end{align}$
After $13$ come $15,17,19,21,23$
$\begin{align}
  & 435-15=420 \\
 & 420-17=403 \\
 & 403-19=384 \\
 & 384-21=363 \\
 & 363-23=340 \\
\end{align}$
After $23$ we get $25,27,29$
$\begin{align}
  & 340-25=315 \\
 & 315-27=288 \\
\end{align}$
So we get $288$, it came from $27$ is subtracted so our required number is $27$.

Note: Remember that we use not asked a number when subtracted $484$ and get $288$ don’t subtract $288$ from $484$ to get the number we have to repeated subtract and find odd term when will be subtracted to get $288$ also we are asked odd and in this we subtract odd, don’t confuse between prime and odd numbers.