Question

How to find the square roots using short cut method?

Answer 1

Step 1: First of all group the number in pairs of 2 starting from the right.
Step 2: To get the ten's place digit, Find the nearest square (equivalent or greater than or less than) to the first grouped pair from left and put square root of the square.
Step 3: To get the unit's place digit of the square root
Remember the following
$\begin{array}{cc}Ifnumber& Uni{t}^{\prime }splacedigitof\\ endsin& thesquareroot\\ 1& 1or9(10-1)\\ 4& 2or8(10-2)\\ 9& 3or7(10-3)\\ 6& 4or6(10-4)\\ 5& 5\\ 0& 0\end{array}$
Lets see the logic behind this for a better understanding
We know,
$1^2=\underset{–}{1}{2}^2=\underset{–}{4}{3}^2=\underset{–}{9}{4}^2=1\underset{–}{6}{5}^2=2\underset{–}{5}{6}^2=3\underset{–}{6}{7}^2=4\underset{–}{9}{8}^2=6\underset{–}{4}{9}^2=8\underset{–}{1}{10}^2=10\underset{–}{0}$
Now, observe the unit's place digit of all the squares.
Do you find anything common?
We notice that,
Unit's place dogot of both $1^{2}and{9}^2$ is 1.
Unit's place dogot of both $2^{2}and{8}^2$ is 4.
Unit's place dogot of both $3^{2}and{7}^2$ is 9.
Unit's place dogot of both $4^{2}and{6}^2$ is 6.
Step 4: Multiply the ten's place digit (found in step 1) with its consecutive number and compare the result obtained with the first pair of the original number from left.
Remember,
If first pair of the original number < the result obtained on multiplication, then select the lesser number out of the two numbers as the unit's place digit of the square root.