In this post we will discuss how to find the square root of a perfect square in less than 15 seconds.
So here is the series of blog posts about smart methods, this is the 11th trick, that will help you solve questions in 5- 10 seconds that would otherwise take 30- 45 seconds.
What is a Square Root?
A square root of a perfect square is a number y such that y2 = z; in other words a square root is a number(y in this case), whose square (the result of multiplying the number by itself, or y × y) is ‘z’. For example: 4 and −4 are square roots of 16 because 42 = (−4)2 = 16.
Example of a Question to Find the Square Root
What is the square root of 3721?
1) 67 2) 61 3) 37 4) 51 5) None of these
Conventional Method to Find the Square Root
The regular method to get the square root of any number is by using the long division method, which as the name suggests is really long and cumbersome and can sometimes take up to 60 seconds for a number. It’s time to ditch this age old method that we learnt in school.
Smart Method to Find the Square Root
Time to master this new method to find square roots, which includes three simple steps coupled with much less calculation.
Step 1 is to look at the digit in the units place and based on that arrive at the various possibilities of the last digit of the square root.
3271 is the number, 1 is the last digit here which implies that the last digit of the square root is either 1 or 9
In Step 2 leave the last two digits of the number and come to the highest perfect square that is closest to the number. This number will be at the tens place for the answer.
After leaving the last two digits we are left with 37 and the highest perfect square that is closest to 37 is 36 (62). Hence the number at the tens place will be 6. This gives us two possible answers 61 or 69
In Step 3 analyze the window in which both the numbers lie and come to the answer based on the value which is the closest.
In this case both the possible answer 61 and 69 lie between 60- 70. Square Root of 60 = 3600 and Square Root of 70 = 4900. The given number 3721 is closer to 3600 when compared to 4900. Therefore, the correct answer is 61
Three steps involving almost no calculations and the square root of a number as big as 3721 is right there!
Watch the video below to see our expert faculty explain this smart method.
Try using this smart method to the square root of these perfect squares.
Question 1: What is the square root of 1849?
1) 43 2) 67 3) 33 4) 57 5) None of these
Question 2: What is the square root of 3249?
1) 67 2) 73 3) 57 4) 67 5) None of these
Remember to leave your answer in the comments below and do tell us how much time you save in finding the square root of these perfect squares.