Let the variables x and y represent any non-negative real numbers.?

Question

Is it true that sqrt(x + y) = sqrt(x) + sqrt(y)?

sqrt(x) = square root of x

Answer 1

No. Consider x=1, y=1. Then √x + √y = 1 + 1 = 2, but √(x+y) = √(1+1) = √2 ≠ 2.

Answer 2

No. This is true only when x = 0 or y = 0 (try plugging in values for x and y and you'll see why.)

In fact, it can be proved that the *only* function f(x) satisfying the identity

f(x + y) = f(x) + f(y)

is the function

f(x) = k*x,

where k is any constant. (such as f(x) = 2x or f(x) = 5x)

This means that it is NOT true that

(x + y) ^ 2 = x ^ 2 + y ^ 2,

2 ^ ( x + y) = 2 ^ x + 2 ^ y,

sin(x + y) = sin(x) + sin(y),

and so on.

Answer 3

nope. but sqrt(x * y) = sqrt(x) * sqrt(y)