## ચાલતી પટ્ટી

શિક્ષક-શિષ્યનો સંબંધ ત્યારે જ શરુ થાય છે જ્યારે બાળકનુ નામ શિક્ષકના હ્રદયરુપી રજિસ્ટરમા નોંધાય છે.-કે.બી.પટેલ~ એ જ લોકો આખરે ફાવી ગયા જે સમયસર બીજને વાવી ગયા.~ રેખાઓમાં રહ્યો અડોઅડ બિંદુઓનો ફાળો મંજિલ બીજું કાઇ નથી,બસ પગલાનો સરવાળો.~ પુસ્તક કરતાં વધારે જીવે એવી કોઈ ઇમારત માનવી બાંધી શકતો નથી.~ ધીમા જવામાં વાંધો નથી,વાંધો ઊભા રહી જવામાં છે.~ લોંખંડ ભલે ગરમ થાય ,પરંતુ હથોડાએ તો ઠંડુ જ રહેવું જોઈએ.~ વર્તમાન જ સાચો સમય છે,બીજા બધા સમય તો માત્ર ભ્રમ છે.~ દરેક કામમાં જોખમ હોય છે,પરંતુ કશું નહીં કરવામાં મોટું જોખમ હોય છે.~ પ્રેરણા એ પ્રિપેઈડ રિચાર્જ કૂપન છે.~ આપનો દ્રષ્ટિકોણ જ પ્રેરણા બને છે.~ શબ્દો કોઈને મારી શકે છે,તો તારી પણ શકે છે.~ જીવન જીતવાની નહીં,પણ જીવવાની વસ્તુ છે.~ ગુસ્સો કરવો સહેલો છે,પણ શાંત રહેવું અઘરું છે.~ સૌથી ઓછું ખર્ચાળ મનોરંજન શ્રેષ્ઠ પુસ્તકોમાંથી મળે છે અને તે કાયમી હોય છે. "Arise,Awake and NOT To STOP Till The GOAL is Reached ”- Swami Vivekananda."

### ગણિત

Fast and Easy Method to Take Square Root- Math Tricks:
Fast and Easy Method to Take Square Root is given here, candidates those who are preparing for banking and all other competitive exams can use this trick in the examination to save time.
POINTS TO REMEMBER:
·         When 22 = 4, then √4 = 2 ·
·         Here 4 is the square of 2 ·
·         2 is the square root of 4 ·
·         A Square of a number can never end with 2, 3, 7 and 8
Table 1:
One’s digit of a square           One’s digit of the square root
1                                                   1 or 9
4                                                    2 or 8
5                                                    5
6                                                    4 or 6
9                                                    7 or 3
To find the square of a number which is a multiple of ‘5’
252 = [2×3] 52 =  25 = 625
i.e., AB2 where B=5
AB2 = [A× next number] B2
For example, 852 = [8×9] 25 = 7225
1152 = [11×12] 25 = 13225
1552 = [15×16] 25 = 24025
This method can be followed for all numbers divisible by 5
TYPE 1: To find the square root of a 3-digit number EXAMPLE: √841 S
STEP 1: Consider the one’s digit of the given number i.e., 1
From Table 1, if the one’s digit of the square is ‘1’ then the square root would either end with ‘1’ or ‘9’
STEP 2: Always ignore the ten’s digit of the given number STEP 3: Now the remaining number other than the one’s and the ten’s digit in the given number is ‘8’
Consider a square-root of a square which is nearer to as well as lesser than ‘8’.
Here it is ‘4’ which is nearer to as well as lesser than ‘8’. Hence the square root of 4 i.e., ‘2’ is taken
STEP 4: we already know the one’s digit of the square root to be either 1 or 9 from STEP 1
Therefore the square root of ‘841’ lies between 21 and 29 STEP 5: Take a number divisible by ‘5’ between 21 and 29, that is ‘25’
252 = [2×3] 25 = 625 Now 625 < 841 252 is itself lesser than 841. Then 212 will be much lesser than 841.
Therefore, the remaining option is ‘29’ √841 = 29
TYPE 2: To find the square root of a 4-digit number EXAMPLE: √8464
STEP 1: Consider the one’s digit of the given number i.e., 4 From Table 1, if the one’s digit of the square is ‘4’ then the square root would either end with ‘2’ or ‘8’
STEP 2: Always ignore the ten’s digit of the given number
STEP 3: Now the remaining numbers other than the one’s and the ten’s digit in the given number is‘84’ Consider a square-root of a square which is nearer to as well as lesser than ‘84’. Here it is ‘81’ which is nearer to as well as lesser than ‘84’. Hence the square root of 81 i.e., ‘9’ is taken
STEP 4: we already know the one’s digit of the square root to be either 2 or 8 fromSTEP 1
Therefore the square root of ‘8464’ lies between 92 and 98 STEP 5: Take a number divisible by ‘5’ between 92 and 98, that is ‘95’
952 = [9×10] 25 = 9025
Now 9025 > 8464 952 is itself greater than 8464.
Then 982 will be much greater than 8464 Therefore, the remaining option is ‘92’ √8464 = 92
TYPE 4: To find the square root of a 5-digit number EXAMPLE: √18769
STEP 1: Consider the one’s digit of the given number i.e., 9 From
Table 1, if the one’s digit of the square is ‘9’ then the square root would either end with ‘3’ or ‘7’ STEP 2: Always ignore the ten’s digit of the given number
STEP 3: Now the remaining numbers other than the one’s and the ten’s digit in the given number is‘187’ Consider a square-root of a square which is nearer to as well as lesser than ‘187’ Here it is ‘169’ which is nearer to as well as lesser than 187. Hence the square root of 169 i.e., ‘13’ is taken
STEP 4: we already know the one’s digit of the square root to be either 3 or 7 from STEP 1
Therefore the square root of ‘18769’ lies between 133 and 137 STEP 5: Take a number divisible by ‘5’ between 133 and 137, that is ‘135’
1352 = [13×14] 25 = 18225
Now 18225 < 18769
1352 is itself smaller than 18769. Then 1332 will be much lesser than 18769
Therefore, the remaining option is ‘137’
√18769 = 137