Is sqrt(a) + sqrt(b) = sqrt (a + b) for all values of a and b?

Question

Is sqrt(a) + sqrt(b) = sqrt (a + b) for all values of a and b?

Answer 1

no, never equal for positive a and b.

in fact, √a + √b > √(a+b) for positive a and b.

Answer 2

sqrt(2+2) is 2. sqrt(2) + sqrt(2) is about 2.828

Answer 3

take 13 for example which is 7+6, so sqrt(7)+sqrt(6)=5.095=sqrt(13)=3.60...so the equality doesn't hold...

conclusion,

sqrt(a)+sqrt(b)<>sqrt(a+b)...for all values of a and b.....done...

Answer 4

yes because of the distributive property with "sqrt"

Answer 5

is sqrt(a) + sqrt(b) is always not equal to sqrt(a + b).

e.g:   sqrt(1) + sqrt(1) = 1 + 1 = 2, but Sqrt (1 + 1) = 1.414

Answer 6

only if a or b is equal to zero.