find the square root of 72080 by long division method
Answers
Answer:
268.477
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, 072080
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 (22 < 7 < 33). Take this number as the divisor and the quotient with the number in the leftmost group as the dividend (07). Divide and get the remainder (3 in this case).
2
2 072080
− 4
3
2.
Bring down the next pair 20. 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 46 × 6 = 276, so we choose the new digit as 6. Get the remainder.
26
2 072080
+ 2 − 4
46 320
− 276
44
3.
Bring down the next pair 80. 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 528 × 8 = 4224, so we choose the new digit as 8. Get the remainder.
268
2 072080
+ 2 − 4
46 320
+ 6 − 276
528 4480
− 4224
256
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 5364 × 4 = 21456, so we choose the new digit as 4. Get the remainder.
268.4
2 072080.00
+ 2 − 4
46 320
+ 6 − 276
528 4480
+ 8 − 4224
5364 25600
− 21456
4144
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 53687 × 7 = 375809, so we choose the new digit as 7. Get the remainder.
268.47
2 072080.0000
+ 2 − 4
46 320
+ 6 − 276
528 4480
+ 8 − 4224
5364 25600
+ 4 − 21456
53687 414400
− 375809
38591
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 536947 × 7 = 3758629, so we choose the new digit as 7. Get the remainder.
268.477
2 072080.000000
+ 2 − 4
46 320
+ 6 − 276
528 4480
+ 8 − 4224
5364 25600
+ 4 − 21456
53687 414400
+ 7 − 375809
536947 3859100
− 3758629
100471
End of long division (upto 3 decimal places).
√72080 = 268.477