SOLUTION: Is sqrt of a + sqrt of b = sqrt a+b for all values of a and b?

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Question 149817: Is sqrt of a + sqrt of b = sqrt a+b for all values of a and b?
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let's assume that sqrt%28a%29%2Bsqrt%28b%29=sqrt%28a%2Bb%29 for all values of a and b. So now let's just pick arbitrary values for a and b. So let's make a=2 and b=3.


sqrt%28a%29%2Bsqrt%28b%29=sqrt%28a%2Bb%29 Start with the given equation.


sqrt%282%29%2Bsqrt%283%29=sqrt%282%2B3%29 Plug in a=2 and b=3


sqrt%282%29%2Bsqrt%283%29=sqrt%285%29 Add 2 and 3 to get 5


1.41421%2B1.73205=2.23607 Take the square root of 2 to get 1.41421. Take the square root of 3 to get 1.73205. Take the square root of 5 to get 2.23607.


3.14626=2.23607 Add 1.41421 and 1.73205 to get 3.14626


Since 3.14626%3C%3E2.23607, this shows us that sqrt%282%29%2Bsqrt%283%29%3C%3Esqrt%282%2B3%29.


So this means that sqrt%28a%29%2Bsqrt%28b%29%3C%3Esqrt%28a%2Bb%29. There are some values that will make it true. For instance a=0 and b=0 are one pair of values, a=1 and b=0 are another. However, in general, the equation sqrt%28a%29%2Bsqrt%28b%29=sqrt%28a%2Bb%29 is not true.