Pythagorean Theorem Question?

Question

if a2 + b2 = c2 ....and the square root of (a2 + b2) = c...why doesn't a +b = c?

Answer 1

Because the square root doesn't 'undo' the squares when there is an addition or subtraction sign involved.

Answer 2

It simply doesn't: try it with the numbers 3, 4 and 5, respectively.
(3*3) + (4 * 4) = (5 * 5): that is 9 + 16 = 25, but 3 + 4 does not equal 5.

If you look at it another way: lets say you start with a, b, and c = 1, 2 and 3 respectively: a+b = c, in this case.
You could multiply each one by a fixed number, and still come up with a+b=c ... for example if you multiply a, b and c by 4, you get 4+8=12... that works.
But if you square each number, you're multiplying a by 1, b by 2 and c by 3: there's no reason for the equation to hold true: 1 + 4 does not equal 9.

Answer 3

suppose a = 3, b = 4, and c = 5 . a + b doesn't equal c but a2 + b2 = c2

the reason is the square root of a sum is NOT the sum of square roots. this operation doesn't distribute

Answer 4

Let a=3, b=4, c=5.

Then 3^2 + 4^2 = 25 = 5^2.

But 3+4 does not equal 5.

Answer 5

1) Given
c^2 = a^2 + b^2

2) Given
c = SQRT(a^2 + b^2)

3) Assume
c = a + b

4) Square both sides
c^2 = a^2 + b^2 + 2ab

3) This contradicts 1) so 3 is false.

Answer 6

because if a2 = a then 4=2 & that dont work....

Answer 7

wow, i never thought about that, ill bug my math teacher with that one tomorrow

very smart !!