## Radicals – hand calculation of square root – pg.5/7

Posted in Math Theory by Lia on 06/01/2013

## Hand calculation of square root

### To calculate by hand a square root we need to consider the radicand number first.

• For the calculation we need to group the radicand’s digits (groups of two digits) on the right and on the left of the decimal point, as shown below:

### The grouping will be: ### The grouping will be: ### By adding zeros as decimals the grouping will be: ### Examples of square roots with the radicand digits’ grouped: ## The calculation Steps:

### Step 1.  Place the number in the radicand area as shown bellow. ### Step 2.  Group the digits of the radicand. ### Step 4. Place the number  found at Step 3 , in our case 3, multiply with itself, and the product,  in our case 9,  on the left hand side of the “Radical calculation divider line” as shown below. ### Step 5. The product obtain at Step 4, in our case 9, is placed under the first group of digit(s), in our case 13. Subtract 9 from 13 as shown. ### Write 7 in the result area as shown. ### Step 10. The difference between the number obtain in Step 7 (number 469), and the number obtain at Step 9 (number 469) is 0. Because the radicand does not have any more digits and the last difference is 0, the calculation is over and the result of this radical extraction is the final number in the ” Radical’s result area”, as shown. ### After Step 9, repeat Steps 7 through 9  until all the radicand’s digits are exhausted. At the end use Step 10 (as in example a)). ### When we arrive at the radicand’s decimal point, we place the decimal point in the result and continue our calculation. ### the rest is: .0050

### The Steps to solve this radical are similar with the steps used to solve the radical in example c). ### the rest is: .0717

### The Steps to solve this radical are similar with the steps used to solve the radical in example d). ### the rest is: .0016

### Because the radicant’s two digit grouping for the last decimal group of digits, on the radicand’s far right hand, it is necessary to add an “0” as shown below. ### the rest is: .0011

### To get a more accurate result, we add decimals,  groups of “00” as shown below. Tagged with: ,