SOLUTION: Are each of the statements below true or false? Explain you answer. Part 1 sq rt (a) + sq rt (b) = sq rt (a+b) Part 2 The numerator and denominator of the following must be m

Algebra ->  Radicals -> SOLUTION: Are each of the statements below true or false? Explain you answer. Part 1 sq rt (a) + sq rt (b) = sq rt (a+b) Part 2 The numerator and denominator of the following must be m      Log On


   

Question 326866: Are each of the statements below true or false? Explain you answer.
Part 1
sq rt (a) + sq rt (b) = sq rt (a+b)
Part 2
The numerator and denominator of the following must be multiplied by sq rt (3) to rationalize 3/3+ sq rt (3) . Explain why.
Thank you for your help!
My thoughts to the first part, the principal square root of a non-negative number is its non-negative square root the symbol sq rt (a) represents the principal square root of a. Therefore a and b can represent any number...
Part one is false.
Part 2 is also false because we would multiply by 1. I am not quite sure if I completely understand...
Again Thank you!!
Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
1) False, See Answer 234051.
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2) False, to rationalize you need to yes multiply by 1 but the numerator and denominator have to equal %283-sqrt%283%29%29 since the denominator is %283%2Bsqrt%283%29%29 so that when you multiply it out the square root terms cancel.
%283-sqrt%283%29%29%283%2Bsqrt%283%29%29=9%2B3sqrt%283%29-3sqrt%283%29-3=6
If you only multiply by sqrt%283%29%7D%7D%2C+then%0D%0A%7B%7B%7Bsqrt%283%29%283%2Bsqrt%283%29%29=3sqrt%283%29%2B3
You still have a square root in the denominator.