Adding Square Roots

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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) + ( 3√2 +√2)     ( Group the like terms)
                                                  = 3√3 + 4√2
 


·     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) = 3√3
√12 = √ (2 *2* 3) = 2√3
√75 = √ (3 *5* 5) = 5 √ 3
√ 48 = √ (2 *2* 2*2*3) =4 √3
√108 = √ (2*2*3*3*3) = 6√3
 
Therefore
√27 + √12 + √75 + √48 + √108 = 3√3+2√3+5 √ 3+4 √3+6√3 =20√3




 

 
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