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Square root of a number is a value that, when multiplied by itself, gives the original number. In other words, the square root of a number x, denoted as [Tex]\sqrt{x}[/Tex], gives the value such that [Tex]\sqrt{x} \times \sqrt{x} = x[/Tex]. For example: The square root of 9 is 3 because 3 × 3 = 9.
In this article, we will discuss various tricks to find the square root of a number in different cases along with some examples for better understanding.
What are Square Roots?Square root of a number is the value that when multiplied by itself yields back the original number. Let us consider the number 25. When 5 is multiplied by itself it returns 25, hence 5 is the square root of 25.
Square root of a number is the value Square root function is denoted by the symbol √ , and it is defined only for non-negative real numbers.
Tricks to Find Square RootTricks to find square roots are used to solve the square root of a number easily and quickly. They are used in making our calculations faster and are helpful in solving difficult questions.
Here are some tricks to easily calculate the square root of a number with different conditions.
Unit Digit TableBelow is the unit digit table which is used to find the unit place of the square root of the given number:
| Number | (Unit digit of Number)2 |
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| 1 | 1 |
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| 2 | 4 |
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| 3 | 9 |
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| 4 | 6 |
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| 5 | 5 |
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| 6 | 6 |
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| 7 | 9 |
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| 8 | 4 |
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| 9 | 1 |
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| 10 | 0 |
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Trick to find Square Root of a 3-digit NumberSquare root of a three-digit will always be a two-digit number. Let us understand the trick to find the square root of a 3-digit number with the help of an example:
- Group the Digits: Group the digits of the 3-digit number into pairs from the right. If there is an odd number of digits, the leftmost digit will form the first pair.For example to find the square root of 361:
- Estimate the Unit Digit: Look at the rightmost pair of digit of the 3-digit number. Use the unit digit table given above to determine the unit digit of the square root of the given number. Unit dit of 361 is 1, hence the square root will have 1 or 9 at the unit place
- Estimate the Tens Digit: Consider the leftmost digit and find the largest perfect square less than or equal to it. Here, the first digit in 361 is 3, hence the largest perfect square less then or equal to 3 is 1.
- Combine the Estimations: Combine the estimations from steps 2 and 3. In this case, the square root of 361 could be either 19 or 11.
Trick to find Square Root of a 4-digit NumberEstimating the square root of a 4-digit number can be approached similarly to the 3-digit numbers, but with some additional considerations due to the larger magnitude. Here is a method to estimate the square root of a 4-digit number:
- Group the Digits: Group the digits of the 4-digit number into pairs from the left.
- Find the Nearest Perfect Square: Find the largest perfect square less than or equal to the first pair of digits. This will help you determine the first digit of the square root.
- Estimate the First Digit: Take the square root of the perfect square found in step 2. This will give you the first digit of the square root.
- Estimate the Remaining Digits: Look at the next pair of digits after the first pair. This will help you estimate the remaining digits of the square root.
- Combine the Estimations: Combine the estimations from steps 3 and 4 to get an approximate square root of the 4-digit number.
- Check the Estimate: Verify the estimate by squaring it and comparing it to the original 4-digit number.
For example, let us estimate the square root of 8836:
- Group the digits: 88 and 36.
- Find the nearest perfect square: The largest perfect square less than or equal to 88 is 92 = 81.
- Estimate the first digit: The square root of 81 is 9.
- Estimate the remaining digits: The next pair is 36.
- Combine the estimations: The square root of 8836 is estimated to be around 93.
- Check the estimate: 932=8649932=8649, which is close to 8836.
Using this method, you can quickly estimate the square root of a 4-digit number without performing complex calculations.
Also Check, Maths Tricks
FAQs on Square Root TricksWhat are square root tricks?Square root tricks are techniques or methods used to quickly estimate or find the square root of a number without performing complex calculations. These tricks often involve patterns, mental math, or simplification methods.
How accurate are square root tricks?Square root tricks provide approximate square roots, so their accuracy depends on the method used and the level of precision required. While they may not always give the exact square root, they can provide a good estimate that is often close to the actual value.
Can square root tricks be used for all numbers?Square root tricks are most effective for perfect squares or numbers with recognizable patterns. While they can provide estimates for non-perfect squares, the accuracy may vary depending on the method used and the specific number.
What are some common square root tricks?Some common square root tricks include the digit by digit method, prime factorization shortcut, estimation method, trailing digit patterns, unit digit method, and mental math techniques.
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