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Square Roots
Welcome to Square Roots! Here, you will learn to calculate the square root of any perfect square.
This method only works if the number is a perfect square, not if it is not one.
Before starting, you should know that-
1. Squares of numbers ending with 1 and 9 end with 1.
2 and 8 end with 4
3 and 7 end with 9
4 and 6 end with 6
0 end with 0
and 5 end with 5.
Let's start with an easy example
1. √576
Step 1: Divide the number into 2 parts. The first part is the first 2 digits from the right and the second part all that is remaining . The orange bar in the image below represents the 2 parts. For the sake of simplicity, lets call 5 as X and 76 as Y.
Step 2: Notice that the first digit (units place) of 576 is 6. Therefore, the units digit in the square root will be either 4 or 6. Having known this, lets move on to the next step.
Step 3: Now, we want to check between which 2 perfect squares is X. X is equal to 5, and hence we know that it comes between 2 square and 3 square. Out of the two numbers (2,3), we shall pick the smaller one, which is 2. Remember these numbers for now (2 and 3).
*if X was equal to a perfect square, for example 9, you would just pick its square root and move on to the next step.
After doing all of this, we have ended up with 4 or 6 as the units digit and 2 as the remaining (tens) digit. Therefore the answer is either 24 or 26.
Step 4: To know the exact value of √576, we need to-
i. Multiply the two numbers from the last step which you kept in your mind. 2*3= 6. If X was a perfect square, then write its square root and then the units digit to get the answer.
ii. Compare the above number to X. If X is smaller than 6, then the answer is 24. (The lower number out of the two possibilities. If X is greater than 6, then 26 is the answer. (the higher number out of the two possibilities). Here, the answer is 24.
2. √15876
Dividing 15876 into 2 parts, we have-
The units digit of the number is 6, hence its square root will end in 4 or 6.
The first part of the number from the number, or X, is 158. 158 comes between 12 square and 13 square. The smaller number is 12, therefore the answer will be 124 or 126.
12*13 is 156, and 158 > 156. Hence, the answer is 126 (the bigger number).
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