Question

square root of 440 by long division method​

Answer 1

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$\implies$The square root of 440, (or root 440), is the number which when multiplied by itself gives the product as 440. Therefore, the square root of 440 = √440 = 2 √110 = 20.97617696340303.

$\large\red{\mid{\fbox{{Explaination}}\mid}}$

• Forming pairs: 04 and 40

• Find a number Y (2) such that whose square is <= 4. Now divide 04 by 2 with quotient as 2.

• Bring down the next pair 40, to the right of the remainder 0. The new dividend is now 40.

• Add the last digit of the quotient (2) to the divisor (2) i.e. 2 + 2 = 4. To the right of 4, find a digit Z (which is 0) such that 4Z × Z <= 40. After finding Z, together 4 and Z (0) form a new divisor 40 for the new dividend 40.

• Divide 40 by 40 with the quotient as 0, giving the remainder = 40 - 40 × 0 = 40 - 0 = 40.

• Now, let's find the decimal places after the quotient 20.

• Bring down 00 to the right of this remainder 40. The new dividend is now 4000.

• Add the last digit of quotient to divisor i.e. 0 + 40 = 40. To the right of 40, find a digit Z (which is 9) such that 40Z × Z <= 4000. Together they form a new divisor (409) for the new dividend (4000).

• Divide 4000 by 409 with the quotient as 9, giving the remainder = 4000 - 409 × 9 = 4000 - 3681 = 319.

• Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 440.

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