Tricks to Solve Tricky Square Root Problems
Are you taking extra time than it actually requires to solve complex square root equations? Well, now with the help of square root tricks you can find the square of numbers very easily and with much less time. Square roots are very important from an examination point of view as it is needed in almost every topic. Tips and tricks always help us to solve mathematical problems easily and swiftly. Therefore, we have here for you a few helpful tips with which you can find the square root of a given number without any kind of help, especially that of a calculator. Without knowing these tips and tricks, it can be time-consuming to find a simple square root of a number.
To begin with, finding the square root of a number, what we have to know first is if the number is a perfect square or not. And we all know that there are two conditions to find if a number is a perfect square or not. First, a number will be a perfect square if it ends with 1, 4, 5, 6, and 9. Second, a number will never be a perfect square if it ends with 2, 3, 7, and 8. These two tips are the most basic tips to find square roots but they are not enough.
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What is a Square Root?
The square root of a number is a value that we get when it is multiplied by itself and produces the original number. For example, when 5 is multiplied by itself we get 25. Thus we can say that 5 is a square root value of 25. In the same way, 4 is the square root value of 16, 6 is the square root value of 36, and 7 is the square root value of 49.
Now, just like a square is a representation of the area of a square that is equal to the side x side, the square root is the representation of the length of the side of a square.
A square root has a symbol that is denoted as ‘\[\sqrt{}\]’. Therefore, we can write square root numbers as\[\sqrt{4}\], \[\sqrt{5}\], \[\sqrt{8}\], \[\sqrt{9}\] etc.
The square root of a number can be rational or irrational. If the square root of a number is an integer, it is a perfect square.
How to Find the Square Root of a Number?
Finding the square root of numbers such as 4, 9, 16, 25, etc. is quite easy, and I’ll tell you why. It is because we all know that from the multiplication table of 1 to 10, the number which is multiplied by itself gives the squares in a two-digit form. But what if a number is in three-digits or four-digits? Well, then it is considered difficult to find the root of these numbers. And that is because we fail to remember the table for higher numbers. So why not know the trick behind to determine the root of larger numbers?
Tricks to Calculate Square Root
You can use the trick to estimate the square root of the perfect square number. To find the square root without long division, you need to know the square root of the first 10 numbers. The square roots of the first 10 numbers are-
Square Root Trick for 4 Digit Numbers
Step 1: Pair the numbers from the right hand side.
Step 2: Compare the unit digits of the numbers in the figure to determine the possible values for the square root of the unit digits.
Step 3: Let's take a look at the first pair of numbers. Let's say "n".
Step 4: Determine the two squares where this number is between √a2 < n < √b2, then a < n < b. Therefore, the tens digit of square roots of the required is "a".
Step 5: As shown in the square table, there are only two numbers and the square does not repeat which is 5 or 10. Confirm that the unit number obtained in step 2 is one of them.
Step 6: After confirming whether the obtained numerical value is 5 or 10, write it as it is. If not, use the following procedure to find the unit digit.
If the unit digit obtained in step 2 is not 5 or 10, the procedure for finding the unit digit is as follows.
Step 7: Multiply a and b.
Step 8: Select b if ab ≤ n, otherwise select a.
Solved Examples
Example 1: Let us consider that we need to find the square root of a large number of 4489.
Step 1: Here, in this number, the unit digit is 9 that means it can be a unit digit of its square root number that is 3 or 7 that is because 32 is 9 & 72 is 49.
Step 2: Now if we consider the first two digits, that is 44, it comes between the squares of 6 and 7 because 62 < 44 < 72.
Step 3: We can expect that in the ten’s digit of the square root of 4489,the lowest amidst the two numbers is 6 and we want to find the unit digit of the square root of the number 4489.
Step 4: Now, we would want to find if 63 or 67 is the square root of 4489.
Step 5: Considering the ten’s digit is 6 and the next number is 7, we have to multiply both the numbers like 6 x 7 = 42 and because 42 is less than 44.
Step 6: Square root of 4489 has to be the bigger number between 63 and 67 i.e. 67.
Therefore,\[\sqrt{4489} = 67\]
Example 2: We can have a look at one more example, the square root of 7056.
Given below is the step by step method:
Now, in this number, the unit digit is 6. All the numbers which have the unit digit as 6 on their square roots. are 4 and 6.
Now consider that the first two digits i.e., 70 come between the squares of 8 and 9 because of 82 < 70 < 92.
Assume that in the ten’s digit of the square root of the 7056, the lowest amidst the two numbers is 8.
So, we have to find the unit digit of the square root of the number 7056. And for that, we have to find between 84 and 86 which one is the square root of 7056.
Since the ten’s digit is 8 and the proceeding number is 9, we have to perform multiplication of both the numbers like 8 x 9 = 72 and because 72 is greater than 70.
The square root of 7056 needs to be a lesser number between 84 and 86 that is 84.
Therefore,\[\sqrt{7056} = 84\]
There are various square roots tricks pdfs which contain more tricks just like this method that you can find on the web. Try to find the square roots of large numbers using these tricks, and you will be able to solve an equation within no time.
Given below is a table of square roots from numbers 1 to 50. This table will help you to solve the problems based on them very easily.
Square Root Table From 1 to 50
FAQs on Square Root Tricks
1. State the difference between square root and under root.
The difference between a square root and an under root can be explained as: The term under root can be used for any of the square root, cube root as well as the nth root. In fact, we can say that under root is just another way to express the nth root. On the other hand, a square root can only be used for a square root. For example, 27 under root to the power 3 will be the cube root of 27, which is 3. On the other hand, the square root of 25 will be 5.
2. What is a square root of a number and how is square root useful?
The square root of a number is a number that, when squared or multiplied to itself will give the given number. This symbol is represented by "\[\sqrt{}\]". Square roots are useful in many ways. In probability theory and statistics, the square root defines a lot of important concepts of standard deviation. It is extremely useful in the formula for the roots of a quadratic equation. There are other concepts based on square roots such as quadratic fields and rings of quadratic integers that are essential in algebra and also in geometry. Carpenters, engineers, and architects also need a square root when they use Pythagorean Theorem basically to lay the foundation plan or floor plan in order to generate an accurate and square building.
3. Give an example of a 3 digit square root trick.
Square root of 169:
Pair the numbers from your right-hand side: 169
The unit position of 169 is 9. Therefore, the unit position of the square root is 3 or 7.
If you look at the first digit 1 here, it's a square of 1 itself. Therefore, the first digit of the square root of 169 is 1. This is because 1 is the minimum value of the square. Therefore, the square root of 169 takes a smaller number between 3 and 7. Therefore, the required square root is 13.