Question

Which number is added to the missing place of \[10000 + 2400 + \_\_\_\_\] to form a square of 112?
a) 100
b) 112
c) 113
d) 144

Answer 1

Hint: Here in this question we have to determine the missing number such that when the missing number is added to the sum of \[10000 + 2400\], then it will be equal to the square of the number 112. Firstly we consider the missing number as x and squaring the number 122. Then by using the simple arithmetic operations the solution is obtained.

Complete step by step solution:
Squares are the numbers, generated after multiplying a value by itself. Whereas square root of a number is the value which on getting multiplied by itself gives the original value.
The square of a number is represented as \[y = {x^2}\], The square root of a number is represented as \[\sqrt y = x\].
Now we consider the given question.
We have to determine the unknown value that should be added for the sum 10000+2400 such that it will be equal to the square of a number 112.
This can be written in the form of an algebraic equation, let unknown value be x.
\[ \Rightarrow 10000 + 2400 + x = {(112)^2}\]
On adding the number 10,000 and 2,400 we have
\[ \Rightarrow 12400 + x = {(112)^2}\]
The number 112 has a power 2, so 112 is multiplied twice. On multiplying 112 twice we have
\[ \Rightarrow 12400 + x = 12544\]
Take 12400 to RHS we have
\[ \Rightarrow x = 12544 - 12400\]
On subtracting 12400 from 12544, so we have
\[ \Rightarrow x = 144\]
Therefore 144 numbers are added to the sum of \[10000 + 2400\], such that it is equal to the square of 112.
Therefore the option d is the correct one.
So, the correct answer is “Option D”.

Note: We can solve this question in another way also. Firstly we determine the square of 112. So the square of 112 is 12544. On subtracting \[10000\] from \[12544\], we have a difference of \[2544\]. On subtracting \[2400\] from \[2544\], the difference will be 144. Or by choosing the numbers from the given options we can determine the value.