To uncover the square root of a perfect square by utilizing the long division method is easy when the numbers room very big since, the method of finding your square root by factorization becomes prolonged and difficult.
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Steps of Long department Method for Finding Square Roots:
Step I: team the digits in pairs, beginning with the digit in the devices place. Every pair and also the continuing to be digit (if any) is referred to as a period. step II: Think the the largest number who square is equal to or simply less than the an initial period. Take it this number as the divisor and also as the quotient. step III: Subtract the product that the divisor and the quotient native the first period and also bring down the next period to the best of the remainder. This becomes the new dividend.Step IV: Now, the brandnew divisor is acquired by taking two times the quotient and also annexing through it a an ideal digit i beg your pardon is likewise taken together the following digit of the quotient, chosen in together a way that the product that the brandnew divisor and this digit is equal to or simply less 보다 the new dividend. Step V: Repeat procedures (2), (3) and also (4) till every the periods have actually been bring away up. Now, the quotient so obtained is the forced square root of the given number.
Examples top top square source of a perfect square by utilizing the long department method
1. Find the square root of 784 through the longdivision method. Solution: marking periods and also using the longdivision method,
Therefore, √784 = 28
2. Evaluate √5329 utilizing longdivision method. Solution: noting periods and using the longdivision method,
Therefore, √5329 =73
3. Evaluate: √16384. Solution: noting periods and using the longdivision method,
Therefore, √16384 = 128.
4. Evaluate: √10609. Solution: noting periods and also using the longdivision method,
Therefore, √10609 = 103
5. Evaluate: √66049. Solution: marking periods and using the longdivision method,
Therefore, √66049 = 257
6. Discover the expense of erecting a fence approximately a square field whose area is 9 hectares if fencing prices $ 3.50 per metre. Solution: Area of the square ar = (9 × 1 0000) m² = 90000 m²Length of each side the the ar = √90000 m = 300 m. Perimeter that the ar = (4 × 300) m = 1200 m. Cost of fencing = $(1200 × ⁷/₂) = $4200.
7. Uncover the least number that must be included to 6412 to do it a perfect square.Solution:We shot to discover out the square source of 6412.
We observe below that (80)² The forced number to be included = (81)²  6412= 6561 – 6412= 149Therefore, 149 need to be included to 6412 to do it a perfect square.
8. What the very least number should be subtracted indigenous 7250 to gain a perfect square? Also, find the square root of this perfect square. Solution: let us shot to uncover the square source of 7250.
This reflects that (85)² is less than 7250 through 25.
So, the least number to be subtracted from 7250 is 25. Forced perfect square number = (7250  25) = 7225And, √7225 = 85.
9. Discover the greatest number of four digits which is a perfect square. Solution Greatest number of four number = 9999. let us shot to uncover the square root of 9999.
This shows that (99)² is less than 9999 through 198.
So, the least number to it is in subtracted is 198. Hence, the required number is (9999  198) = 9801.
10. What the very least number need to be included to 5607 to do the sum a perfect square? find this perfect square and also its square root. Solution: We shot to discover out the square root of 5607.
We observe below that (74)² The required number to be added = (75)²  5607 = (5625 – 5607) = 18
11. Uncover the least variety of six number which is a perfect square. Find the square source of this number. Solution: The least number of six number = 100000, i beg your pardon is no a perfect square. Now, us must find the least number i m sorry when included to 1 00000 provides a perfect square. This perfect square is the required number. Now, we uncover out the square source of 100000.
Clearly, (316)²
Therefore, the the very least number to be included = (317)²  100000 = 489. Hence, the compelled number = (100000 + 489) = 100489. Also, √100489 = 317.
12. Uncover the the very least number that need to be subtracted from 1525 to do it a perfect square. Solution: Let us take the square root of 1525
We watch that, 39²
Therefore, to get a perfect square, 4 need to be subtracted native 1525. as such the compelled perfect square = 1525 – 4 = 1521
● Square Root
Square Root
Square source of a Perfect Square by utilizing the prime Factorization Method
Square root of a Perfect Square by using the Long division Method
Square root of numbers in the Decimal Form
Square source of Number in the portion Form
Square source of number that space Not Perfect Squares
Table of Square Roots
Practice test on Square and also Square Roots
● Square Root Worksheets
Worksheet on Square Root utilizing Prime factorization Method
Worksheet top top Square Root making use of Long department Method
Worksheet ~ above Square root of number in Decimal and portion Form
8th Grade mathematics Practice From Square source of a Perfect Square by using the Long division Method to house PAGE
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