We get22.360up to three decimal places.

Explanation:

As the given number is not a perfect square, the square root of this number will be a decimal number.We must, therefore, state the accuracy to which the square root is to be calculated.

Suppose we need to calculate the√500to an accuracy of three decimal places.

Step 1. Make pairs of digits starting from Units place.we get5¯¯¯¯00.

Step 2. Consider the unpaired digit and calculate the nearest digit which is just lower than the square root of this digit. We consider5.The nearest digit is2as32=6>5.

We get first digit of the answer. Workout the remainder which=1. Bring down the next pair which is¯¯¯¯00. Makes the dividend=100. Also add the answer digit to the divisor. We have2+2=4

Step 3. Place highest digit in units place of divisor to make the divisor which will divide dividend100. We see that it can be divided with2×42.∴3×43>100.Complete the division. Nearest digit is2. Complete the division and obtain remainder.=100−84=16. Also add the answer digit so obtained to divisor. We get42+2=44for the next step.

Step 4. Next we have decimal in the original number. Place it after the quotient22and bring a pair of zeros down. The dividend becomes1600

Continue steps till three places of decimal.

We see that in the Step 5. Number remaining is304.Adding two zeros makes it30400We are not able to divide the dividend because even with digit1placed at units place of divisor the product of quotient digit and divisor is>the dividend. We place a0in the quotient place and add two zeros to the dividend.