Dear Aspirants,
Today we will learn the easy trick of square root because this topic is very important not only based on competitive exams but also during schooling studies, through this trick or method we can easily find the root of the perfect square number in a quick time. So let's know what's the method.
Square Root
By this square root trick, we can find the perfect square number square root or we can estimate the square root. For this, we must have remembered the last digit of squaring number between 1 to 9.
Square → Last Digit
of Number after squaring the No.
1² = 01 → 1
2² = 04 → 4
3² = 09 → 9
4² = 16 → 6
5² = 25 → 5
6² = 36 → 6
7² = 49 → 9
8² = 64 → 4
9² = 81 → 1
For this trick, we must remember the unit digit of the square of the number. If a number consists of either 2, 3, 7 or 8 as its unit place then we can not calculate the perfect square root of such number. Let.s understand by the example.
3-Digit Square Root
Ex. 1) Find √729
Solution:
Step 1: We have to first see that the unit digit of the one whose square root we have been asked is not 2, 3, 7 or 8, if it is not, then we can find its perfect square root.
Step 2: After this, we have to make a pair going from right to left, always two digits on the right side are made a pair and the remaining digits are made a pair. In this question, 29 will be a pair and 7 will be a pair.
√7 29
Step 3: In the above question, the unit digit is 9. After this, we have to see where 9 comes in the Last Digit after squaring the number (table). In this case 3 or 7, since 3² = 09 and 7² = 49, the last digit of our answer will be either 3 or 7.
√7 29 = __ 3 / __7
Step 4: Because from the above step we have taken out the unit digit of answer from 29 pair will be 3 or 7 Now for the left pair 7, we have to see which is the square of the number less than or equal to 7 since we know that 2² = 4 and 3² = 9 is.
2² = 4 ≤ 7 < 3² = 9
Step 5: Since the number 4 is smaller than 7 square root of 4 is 2, so 2 will come in the ten's digit of the answer. because 2² = 4 and 3² = 9 and the number 9 is greater than 7 so that's wrong we have to take 2 which square means 4 is smaller than 7 we always take lesser or equal no. in this case 7's lower squaring is the answer in ten's digit place.
√7 29 = 2 3 / 2 7
This means that our answer will be either 23 or 27.
Step 6: Now we have to find the exact number, then we will see how much the square of 25 which comes roughly in the middle of both. Since we know from the earlier article how to find 25² fast, we can say that 25² = (2 × 3) 5² = 6 25 which is less than 729 so our answer will be 27 because we have 729 If the square root is asked, it is greater than 625, then from our estimation, the answer will be 23 or 27 out of 27.
Read this for an easy trick of the square of a number in which the last digit is 5.
It can be found in short like below,
4-Digit Square Root
Ex. 2) Find √4624Solution: As we know that the pair is made first, a pair of two digits is made from the right side and a pair of the remaining digits from the left side.
√46 24 Now we will see that the unit digit 4 in this question comes in the unit digit after square of which numbers from 1 to 9, then according to the table it happens in 2 or 8 (2² = 4 and 8² = 64) It means the unit digit of the answer will be 2 or 8. Now the left pair is 46. We will find the square of the number which is less than 46 since 6² = 36 and 7² = 49. Digit 36 is less than 46 so √46 24 = 62 or 68. To find Exact, use the above Ex.1 method like find 65² or there is another method. Since the numbers 62 or 68 are around 60 and 70, we see 60² and 70² which has nearly 4624.
60² = 3600 and 70² = 4900 because 70 is around 4624. So √46 24 = 68 answer.
Ex. 3) Find √1681
Solution:
- Since the pair is made first, a pair of two digits is made from the right side and a pair of the other is made from the left side. After that, the unit digit is found.
√16 81 = _1 / _9
- In the Remaining pair, it is seen that we will see the square of such a number which is less than or equal to 16. In this context 4² = 16 is equal, so
√16 81 = 41 / 49
- Since 40² = 1600 and 50² = 2500, the number 1681 is near 1600 which means 40² is near 1681 so the answer will be 41.
√16 81 = 41
5-Digit Square Root
Ex. 4) Find √42436
Solution:
- First, a pair is made, so a pair of two digits is made from the right side and a pair of the remaining other is made. After that, the unit digit is found.
- In the Remaining pair, it is seen that we will see the square of such a number which is less than or equal to 424. In this context, 20² = 400 and 21² = 441, so 400 number is less than 424, so
- Since we can easily find the square of 205 through trick
- Number 42436 is greater than number 42025 so the answer will be 206.
√424 36 = 206
The fast calculation can be done with consistent practice. I think you must have understood this method, if you liked this article or have any doubt, then tell us by comment and share more and more because Knowledge increases by sharing. The article on the Non-Perfect Square Root Trick will be soon.
Thank you for reading this article
Have a Nice Day
Your Gyaan INside
Tags:
Calculations Tricks