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**Sample:** Square root of 5 using division method

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, 05

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 (**2**^{2} < 5 < 3^{3}). Take this number as the divisor and the quotient with the number in the leftmost group as the dividend (05). Divide and get the remainder (1 in this case).

2 | ||||

2 | 05 | |||

− | 4 | |||

1 |

2. Put the decimal point.

3.

**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 42 × 2 = 84, so we choose the new digit as **2**. Get the remainder.

2.2 | ||||

2 | 05.00 | |||

+ | 2 | − | 4 | |

42 | 100 | |||

− | 84 | |||

16 | ||||

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 443 × 3 = 1329, so we choose the new digit as **3**. Get the remainder.

2.23 | ||||

2 | 05.0000 | |||

+ | 2 | − | 4 | |

42 | 100 | |||

+ | 2 | − | 84 | |

443 | 1600 | |||

− | 1329 | |||

271 | ||||

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 4466 × 6 = 26796, so we choose the new digit as **6**. Get the remainder.

2.236 | ||||

2 | 05.000000 | |||

+ | 2 | − | 4 | |

42 | 100 | |||

+ | 2 | − | 84 | |

443 | 1600 | |||

+ | 3 | − | 1329 | |

4466 | 27100 | |||

− | 26796 | |||

304 | ||||

End of long division (upto 3 decimal places).

√5 = 2.236

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