Question

Explain with reason whether the given number is perfect square or not: 5050

Answer 1

Hint:
We can randomly select a number such that its square comes in the range of the given number. If the square of the number is less than the given number, we can take the square of the number next to it. We can repeat this step until we get the square of the number we took is equal to the given number or greater than that. If the square of any of the numbers is equal to the given number, the number will be a perfect square.

Complete step by step solution:
We need to check whether 5050 is a perfect square or not.
Let us consider the number 60. Then its square root is given by, $60 \times 60 = 3600$
This value is too low compared to the given value.
So, we can consider the number 70. Then its square root is given by, $70 \times 70 = 4900$ .
It is less than the given number. So, we can take the number next to 70, which is 71.
Then its square is given by, $71 \times 71 = 5041$
It is also less than the given number. So, we can take the next number, which is 72.
Then its square is given by, $72 \times 72 = 5184$ . This number is greater than the given number.
From this we can conclude that there is no number between 71 and 72 that gives the number 5050 when squared.

So, 5050 is not a perfect square.

Note:
Alternate method to solve this problem is by factorising.
We can factorize the given number 5050 into prime numbers.
 \[ \Rightarrow 5050 = 5 \times 5 \times 2 \times 101\]
Now we can take the square root.
 \[ \Rightarrow \sqrt {5050} = \sqrt {5 \times 5 \times 2 \times 101} \]
 \[ \Rightarrow \sqrt {5050} = 5 \times \sqrt 2 \times \sqrt {101} \]
As the square root of both 2 and 101 are not whole numbers, they are not perfect squares.
So, the given number is also not a perfect square.