Square & Square Root

Square 

Square Upto 25

1 1 14 196
2 4 15 225
3 9 16 256
4 16 17 289
5 25 18 324
6 36 19 361
7 49 20 400
8 64 21 441
9 81 22 484
10 100 23 529
11 121 24 576
12 144 25 625
13 169    

 

Square Root

Square Root upto 10

1 1.000
2 1.414
3 1.732
4 2.000
5 2.236
6 2.449
7 2.646
8 2.828
9 3.000
10 3.162

 

Methods of Finding Square Root

1. Factor Method

Steps:
1. Find the Prime Factors of the number.
2. Make the pair of same factors.
3. Choose one factor out of every pair.
4. Find the product of the choosed number which is the required square root of the number.
Example:

 

2. Division Method

Steps:

1. Group the digits in pairs, starting with the digit in the units place. Each pair and the remaining digit (if any) is called a period. 
2. Think of the largest number whose square is equal to or just less than the first period. Take this number as the divisor and also as the quotient. 
3. Subtract the product of the divisor and the quotient from the first period and bring down the next period to the right of the remainder. This becomes the new dividend. 
4.Now, the new divisor is obtained by taking two times the quotient and annexing with it a suitable digit which is also taken as the next digit of the quotient, chosen in such a way that the product of the new divisor and this digit is equal to or just less than the new dividend. 
5. Repeat steps (2), (3) and (4) till all the periods have been taken up. Now, the quotient so obtained is the required square root of the given number.
Example:

Example 1: √66049

therefore, √66049 = 257

Example 2: √5329

Therefore, √5329 =73

Questions Asked from this Chapter:

 

Question Type 1: Based on Calculation of Square Root of a Number or Expression

Question:

Answer:

Questions Type 2: Based on Finding the Unit Digit in Square Root

Question:

Answer:

Question Type 3: Based on Making a Number Perfect Square

Question:

Answer: