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

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

Start with the given equation.

Plug in and

Add 2 and 3 to get 5

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.

Add 1.41421 and 1.73205 to get 3.14626

Since , this shows us that .

So this means that . There are some values that will make it true. For instance and are one pair of values, and are another. However, in general, the equation is not true.
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