simplify root under 7624- 7824
Answers
Answer:
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, 0240
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 (11 < 2 < 22). Take this number as the divisor and the quotient with the number in the leftmost group as the dividend (02). Divide and get the remainder (1 in this case).
1
1 0240
− 1
1
2.
Bring down the next pair 40. 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 25 × 5 = 125, so we choose the new digit as 5. Get the remainder.
15
1 0240
+ 1 − 1
25 140
− 125
15
3. Put the decimal point.
4.
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 304 × 4 = 1216, so we choose the new digit as 4. Get the remainder.
15.4
1 0240.00
+ 1 − 1
25 140
+ 5 − 125
304 1500
− 1216
284
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 3089 × 9 = 27801, so we choose the new digit as 9. Get the remainder.
15.49
1 0240.0000
+ 1 − 1
25 140
+ 5 − 125
304 1500
+ 4 − 1216
3089 28400
− 27801
599
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 30981 × 1 = 30981, so we choose the new digit as 1. Get the remainder.
15.491
1 0240.000000
+ 1 − 1
25 140
+ 5 − 125
304 1500
+ 4 − 1216
3089 28400
+ 9 − 27801
30981 59900
− 30981
28919
End of long division (upto 3 decimal places).
√240 = 15.491
Step-by-step explanation: