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8 votes
Without using a calculator, approximate the following root to three decimal places: √3.

Show the steps you took to get your approximate value. ​

User Frej Connolly
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1 Answer

20 votes
20 votes

Answer:

1.732


Step 1: To begin, we write 3 as 3.000000 and group the 0s after the decimal point in pairs of 2 from left to right as shown below. (for digits to the left of the decimal point, pair them from right to left)

Step 2: Think of a number which when multiplied with itself, is less than or equal to 3. In this case, that number would be 1.

Step 3: Dividing by 3 by 1 with quotient set as 1, we get a remainder of 2.

Step 4: Drag a pair of 0’s down and fill it next to 2 to make the dividend 200.

Step 5: The divisor which is 1 here is added with itself and written below. Now, we have 2X as the new divisor, and we need to find a value of X that makes the product of 2X × X less than or equal to 200. In this case, 27 is the required value

Step 6: The number 7 is placed in the quotient after a decimal place. The new divisor for the next division will be 2X + X, which is 34 in this case.

Proceeding in the same manner and repeating from step 4, we can calculate the rest of the decimals.

User Mahdi Zarei
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