SOLUTION: Are each of the statements below true or false? Explain your answer. √a + √b = √(a+b). Explain why. The numerator and denominator of the following must be

Question 474691: Are each of the statements below true or false? Explain your answer.
√a + √b = √(a+b). Explain why.
The numerator and denominator of the following must be multiplied by √3 to rationalize
3
-----------. Explain why.
3 + √3

Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
1. Statement is false because if we square both sides we get

which does not hold for all real a,b.

2. It must be multiplied by 3 - sqrt(3), not just sqrt(3). This is because the denominator becomes a rational number (applying difference of two squares).
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SOLUTION: Are each of the statements below true or false? Explain your answer. &#8730;a + &#8730;b = &#8730;(a+b). Explain why. The numerator and denominator of the following must be

SOLUTION: Are each of the statements below true or false? Explain your answer. √a + √b = √(a+b). Explain why. The numerator and denominator of the following must be