Adding Square Roots

Adding Square Roots If a and x are two real numbers and a^2 = x then a is called the square root of x and is written as a= x or x^ (1/2). Clearly square root of x (i. e. x) is such a number whose 2nd power equal to x i.e., ( x) ^2 = x. For example: - Square root of 25 i.e., 25 = 5 (Since 5^2 =25) Note: - Since 5^2 = 25 therefore 25 = 5 Again, (-5) ^2 = 2 hence 25 = -5 Therefore, it is evident that both 5 and (-5) are square roots of 25. For this reason, by square root of a real number x we mean x (i.e., + x and - x). Example of adding square roots: - Simplify 2 3 + 3 2 + 3 + 2 Solution: - 2 3 + 3 2 + 3 + 2 = (2 3 + 3) + ( 32 +2) ( Group the like terms) = 33 + 42 Example 2: - 27 + 12 + 75 + 48 + 108 Solution: - Try to reduce the radical and make it a smaller number as much as possible as shown 27 = (3 *3*3) = 33 12 = (2 *2* 3) = 23 75 = (3 *5* 5) = 5 3 48 = (2 *2* 2*2*3) =4 3 108 = (2*2*3*3*3) = 63 Therefore 27 + 12 + 75 + 48 + 108 = 33+23+5 3+4 3+63 =203