Dear Aspirants,
Previously we learned the easy trick of the Perfect Square root Number. Now sometimes a problem occurs when there is not perfect square number and we have to find the approx square root of the number, today we will learn the Non-Perfect Square Root Number Trick.
Non-Perfect Square Root for Single and 2-digit Numbers
For single-digit and 2-digit numbers, we can find approx. the square root of a number. Formulas are given below, by that formula, we easily find values of √7 and √19 etc.
- √(A+B) = √A + (B/2√A)
- √(A-B) = √A - (B/2√A)
Solution: √7 = √(9-2) where, A = 9 & B = 2
by the formula √(A-B) = √A - (B/2√A)
→ √(9-2) = √9 - (2/2√9)
→ √7 = 3 - (1/3)
→ 3 - 0.3333
→√7 = 2.65 approx.
Find values of √19
Solution: √19 = √(16 + 3) where, A = 16 & B = 3
by the formula √(A+B) = √A + (B/2√A)
→ √(16+3) = √16 + (3/2√16)
→ √19 = 4 + {3/(2×4)}
→ 4 + 3/8
→ 4 + 0.375
→√19 = 4.375 approx.
Find values of √26
Solution: √26 = √(25 + 1) where, A = 25 & B = 1
by the formula √(A+B) = √A + (B/2√A)
→ √(25+1) = √25 + (1/2√25)
→ √26 = 5 + {1/(2×5)}
→ 5 + 1/10
→ 5 + 0.1
→√26 = 5.1 approx.
3-Digit Number Square Root
For 3-Digit Number Square Root, we know in the previous Square root Trick for Perfect Square Number blog 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
In the above Last Digit after squaring the No. there is no digit of 2, 3, 7, 8 so if the unit digit of a number is 2, 3, 7, 8 which we have to find a square root that means the square root of that number is definitely a non-perfect number. So we can predict the approx answer from the given options. Let's understand by the examples.
Ex. 1) Find √727 and give the answer.
Options:
- 27.96
- 25.78
- 26.96
- 24.93
Solution:
As we know in the previous blog on this subject we 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.
we make pair of √7 27 but there is 7 in the unit digit, so we assume close to 727 number and which unit digit is 1, 4, 5, 6 or 9 the number 726 is nearest to 727 and its unit digit is 6. Now we can reach square root near √726
Now our unit digit is 6. After this, we have to see where 6 comes in the Last Digit after squaring the number (table). In this case, 4 or 6 since 4² = 16 and 6² = 36, the last digit of our estimated answer will be either 4 or 6.
√7 26 = __ 4 / __6
we have taken out the unit digit of answer from 26 pair will be 4 or 6 Now for the left pair 7, we have to see which is the square of the number less than or equal to 7 as we know that 2² = 4 and 3² = 9 is.
2² = 4 ≤ 7 ≤ 3² = 9
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.
√7 26 = 24 / 26
This means our approx answer will be either 24 or 26.
Now we have to find the exact number 24 or 26, then we will see how much the square of 25, comes in the middle of both 24 & 26. Since we know from the earlier article for an easy trick of the square of a number in which the last digit is 5. how to find 25² quickly, we can say that 25² = (2×3) 5² = 6 25
Because 24² ≤ 25² = 625 ≤ 26²
so our answer will be 26 because 726 is greater than 625 from our estimation, the answer will be 26.
That means
√726 = 26.xxx something So also √727 is 26.xxx
Note: Now we can also check √729 by the above method
It can be short like below,
- √7 29 = __ 3 / __7 So, 2² = 4 ≤ 7 ≤ 3² = 9
- √7 29 = 2 3 or 2 7
- 25² = 625 < 729 Hence the answer will be 27.
So from the options Option 3. 26.96 is the answer.
√726 = 26.96
4-Digit Number Square Root
Ex. 2) Find approx value of √8642
Options:
- 96
- 93
- 91
- 97
Solution: As we know that the pair is made first, two digits are made from the right side and a pair of the remaining digits from the left side.
√86 42
there is a digits 2, 3, 7, and 8 in the unit digit so we have to find a square root, which means the square root of that number is definitely a non-perfect number. So we take a number which is near 8642 by which we can find the root of the number so we take 8641.
So we can find √8641
- 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.
√86 41 ≈ _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, 9² = 81 is less than 86, so
√8641 ≈ 91 / 99
- As we know 90² = 8100 and 100² = 10000, number 1681 is near 1600 which means 40² is near 8641 so the answer will be approx 91.
√8641 ≈ 91 but we don't know whether it is right or wrong it is the approx value but the given options are so close and we have to find √8642 so 91 is not the answer. Answer must be greater than 91, also we can find quickly 91² by the trick Square Trick of numbers between 90 & 100 and Square of any Digit Number Method
Finding (91)²
Step 1: 100 - 91 = 09 | (9)² = 81 (right hand side digits)
Step 2: 91 - 9 = 82 (left hand side digits)
Step 3: Answer 8281
(91)² = 8281 and we have to find √8641. Since 8641 is more than 8281 so the answer is definitely a little bit more than 91 so √8641 ≈ 93
Ans: √8642 ≈ 93 (Option 3)
Also read: Square Trick of numbers between 100 & 110
5-Digit Number Square Root
Ex. 2) Find approx value of √12463
Options:
- 112
- 108
- 122
- 118
Solution:
- First of all, we have to take a number which is near 12463 so we take 12464 now we can find the unit digit number of its square root.
- After that 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 124. In this context, 11² = 121 and 12² = 144, so 121 is less than 124, so
- Now let's see the options both 112 and 118 are given in the option so we have to take one final step to find approx. answer. We can easily find the square of 115 through a trick
- Number 13225 is greater than number 12462 so the answer will be 112.
Ans: √12462 ≈ √12463 ≈ 112
Option 1: √12463 ≈ 112
By this above estimation method, you can find Non-Perfect Square Root easily. I think you understand this method, if you liked this article or have any doubt, then comment and share more and more because 'Knowledge increases by sharing.
Thank you for reading this article
Have a Nice Day
Your Gyaan INside
Tags:
Calculations Tricks