FINDING SQUARE ROOTS BY Prime Factorization

In this method, we need to list the prime factors of the given number and then make the pair of two same numbers.

Then write one number for each pair and multiply to find the square root.

Example

Calculate the square root of 784 using prime factorization method.

Solution:

List the prime factors of 784.

784 = \underline{2\times2}\times\underline{2\times2}\times\underline{7\times7}
\sqrt{784}=2\times2\times7=28

Finding Square Root by Long Division Method

Steps involved in finding the square root of 484 by Long division method:


Step 1: Place a bar over every pair of numbers starting from the digit at units place. If the number of digits in it is odd, then the left-most single-digit too will have a bar.


Step 2: Take the largest number as divisor whose square is less than or equal to the number on the extreme left. Divide and write quotient.

Step 3: Bring down the number which is under the next bar to the right side of the remainder.

Step 4: Double the value of the quotient and enter it with a blank on the right side.

Step 5: Guess the largest possible digit to fill the blank which will also become the new digit in the quotient, such that when the new divisor is multiplied to the new quotient the product is less than or equal to the dividend.

The remainder is 0, therefore,  \sqrt{484}=22 .

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