Square root by Long Division Method

 Square root by Long Division Method

Example1

1)find the square root of 14996

Step 1

Separate the digits from right to left once in two digits

                            1 49 96 

here, we got 1 before the first space

Step2

Now we have to find the square of a number such that it must be <=1

here, 1*1 =1

now, let we do this by long division

here, we subtracted and got the remainder as 0,

Step 3

Now we have to get down the next pair (49) and quotient 1 as to be multiplied by 2.

Step 4

Now we have to take same number at the two places where we mentioned _

and then we have to find the product where that product must be = or < 49.

 then subtract and we got the remainder 5

Step 5

Again bring down the next pair and repeat from step 3. that is multiply the quotient by 2.

    

Hence Square root of (14996) = +/- 122 with remainder 112

Example 2

2) find the square root of 119025

Step1

11 90 25

Step 2

Step 3

  we multiplied quotient 3 by 2=6

step 4

Step 5

Hence, square root (119025) = +/- 345

Square Root

 Square Root

       A square root of a number is a value that, when multiplied by itself , gives the number .

√a²=√a*a = a  (a² = a*a)

Note

a² = -a * -a (since - * - = +)

so, 

√a²=√-a*-a = -a

Hence,

√a²= a or -a

Example

1) Find a square root of 25 or find √25

25 = 5* 5  or  25 = -5 * -5

√25 = √5*5 = 5

or 

√25 = √-5*-5 = -5

hence, √25 = 5 or -5

2) Find a square root of 9 or √9

9 = 3*3 or 9 = -3 * -3

√9 = √3*3 = 3

or 

√9 = √-3*-3 = -3

3) find the square root for 576

 

 

√ 576 = 24 or -24

Square Of a Number

 Square of a Number

    To square a number, just multiply it by itself.

That is,

a² = a*a
also, we can write it as
 a^2 = a*a (^ is the symbol of exponent)

Example

1) Find a square of 2

here the number is 2

to find a square of a number we have to multiply that number by itself

square of 2 = 2*2 =4

that is, 2^2=2*2=4

2) Find a square of 3

3²=3*3=9

3) Find a square of 7

7²=7*7 = 49

4) Find a square of (-5)

(-5)² = -5 * -5 = 25 

Note 

- * - = +  (-3 * -3 = 9)

- * + = -  (-3 * 3 = -9)

+ * - = -  (3 * -3 = -9)

+ * + = + (3 *  3 = 9)

5) Solve (8-4)²

8-4 = 4

(8-4)² = 4² = 4*4 = 16

6) Solve (15-25)²

15-25 = -10

(15-25)² = (-10)² = -10 * -10 = 100

Note

5-3 = 2

-5-3 = -8

-5+3 = -2

5+3 = 8