PROPERTIES OF SQUARE ROOTS

1. If two or more numbers multiplied with square roots, you can take the square root once and multiply the numbers inside the square root. 

√m x √n = √(m x n)

2. If two numbers are in division with square roots, you can take the square root once and divide the numbers inside the square root. 

√m/√n = √(m/n)

3. One number can be taken out of the square root for every two same numbers multiplied inside the square root. 

√(m  x m) = m

√4 = √(2 x 2) = 2

4. Square root of a number can be written as exponent 1/2. 

√m = m^1/2

5. Addition and subtraction of two or more numbers with square roots can be performed with like radicands only. (Radicand is the number inside the square root)

For example, 9√2 and 4√2 can be added or subtracted. Because the numbers inside the square roots are same. 

9√2 + 4√2 = 13√2

9√2 - 4√2 = 5√2

6. If a square root is moved from side of the equation to the other side, it will become square. 

√x = a

x = a²

7. If a square is moved from side of the equation to the other side, it will become square root. 

y² = b

y = √b

8. If the digit in one's place of a number is 2, 3, 7 or 8, then the number can not be a perfect square. So the square root of such numbers will be irrational. 

For example, √23  =  4.795831.........

9. If a number ends with odd number of zeros, then, the square root of the number will be irrational.

For example, √3000  =  54.772255.......

10. The square of a perfect square is always a rational number.

√4 = √(2 x 2) = 2

√49 = (7 x 7) = 7

11. The square root of an even perfect square number is always even and the square root of an odd perfect square number is always is odd.

For example, 

√144  =  144

√225  =  15

12. Square root of a negative number is considered to be an imaginary value. 

For example, √(-9), √(-12). 

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