Square Root Using Long Division
Square Root Using Long Division
When the square numbers are very large, the method of finding their square roots by prime factorization becomes very lengthy and difficult also. In such cases, we use the method of long division to find the square root. We follow the following step wise procedure to find the square root of squares by the long division method.
Procedure:
STEP I Obtain the number whose square root is to be computed.
STEP II Place bars over every pair of digits starting with the units digit. Also, place a bar on one digit (if any) not forming a pair on the extreme left. Each pair and the remaining one digit (if any) on the extreme left is called a period.
STEP III Think of the largest number whose square is less than or equal to the first period. Take this number as the divisor and the quotient.
STEP IV Put the quotient above the period and write the product of divisor and quotient just below the first period.
STEP V SUbtract the product of divisor and quotient from the first period and bring down the next period to the right of the remainder. This becomes the new dividend.
STEP VI Double the quotient as it appears and enters it with a blank on the right for the next digit, as the next possible divisor.
STEP VII Think of a digit, to fill the blank in step VI, in such a way that the product of the new divisor and this digit is equal to or just less than the new dividend obtained in step V.
STEP VIII Subtract the product of the digit chosen in step VII and the new divisor from the dividend obtained in step V and bring down the next period to the right of the remainder. This becomes a new dividend.
STEP IX Repeat steps, VI, VII, and VIII till all periods have been taken up.
STEP X Obtain the quotient as the square root of the given number.
The following illustration will illustrate the above procedure.
Illustration: Find the square root of 4937284 by the long division method.
(i) 4937284
SOLUTION
Find the last divisor while calculating the square root of 54756 using the long division method. | |||
| Right Option : B | |||
| View Explanation | |||
Find the divisor at the third stage in the square root of 12544 while calculating its square root using the method of long division. | |||
| Right Option : B | |||
| View Explanation | |||
The number of digits in the square root of 298116 is____ | |||
| Right Option : C | |||
| View Explanation | |||
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