square root of 320625 by long division method
Answers
Answer:
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Answer:
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Step-by-step explanation:
Group the digits into pairs (For digits to the left of the decimal point, pair them from right to left. For digits after decimal point, pair them from left to right).
Thus we have, 320625
Perform division as per steps shown below:
1.
Find the largest number whose square is less than or equal to the number in the leftmost group (55 < 32 < 66). Take this number as the divisor and the quotient with the number in the leftmost group as the dividend (32). Divide and get the remainder (7 in this case).
5
5 320625
− 25
7
2.
Bring down the next pair 06. Add the divisor with the quotient and enter it with a blank on its right. Guess a 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. In this case 106 × 6 = 636, so we choose the new digit as 6. Get the remainder.
56
5 320625
+ 5 − 25
106 706
− 636
70
3.
Bring down the next pair 25. Add the divisor with the quotient and enter it with a blank on its right. Guess a 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. In this case 1126 × 6 = 6756, so we choose the new digit as 6. Get the remainder.
566
5 320625
+ 5 − 25
106 706
+ 6 − 636
1126 7025
− 6756
269
4. Put the decimal point.
5.
Remember: A decimal number, say, 3 can be written as 3.0, 3.00 and so on. Bring down the next pair 00. Add the divisor with the quotient and enter it with a blank on its right. Guess a 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. In this case 11322 × 2 = 22644, so we choose the new digit as 2. Get the remainder.
566.2
5 320625.00
+ 5 − 25
106 706
+ 6 − 636
1126 7025
+ 6 − 6756
11322 26900
− 22644
4256
6.
Remember: A decimal number, say, 3 can be written as 3.0, 3.00 and so on. Bring down the next pair 00. Add the divisor with the quotient and enter it with a blank on its right. Guess a 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. In this case 113243 × 3 = 339729, so we choose the new digit as 3. Get the remainder.
566.23
5 320625.0000
+ 5 − 25
106 706
+ 6 − 636
1126 7025
+ 6 − 6756
11322 26900
+ 2 − 22644
113243 425600
− 339729
85871
7.
Remember: A decimal number, say, 3 can be written as 3.0, 3.00 and so on. Bring down the next pair 00. Add the divisor with the quotient and enter it with a blank on its right. Guess a 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. In this case 1132467 × 7 = 7927269, so we choose the new digit as 7. Get the remainder.
566.237
5 320625.000000
+ 5 − 25
106 706
+ 6 − 636
1126 7025
+ 6 − 6756
11322 26900
+ 2 − 22644
113243 425600
+ 3 − 339729
1132467 8587100
− 7927269
659831
End of long division (upto 3 decimal places).
√320625 = 566.237