Question

If root x + root y = root 45 and x and y are positive integers, then find the value of root x + y.

Answer 1

x = 5

y = 20

sqrt(x + y) = sqrt(25) = 5

Explanation:

I think this is one of those things where you think you've been tricked and when you see the answer, you know you have.

The root of 45 = root (5 * 3 *3) = 3sqrt(5)

Now you need to find some way of making x and y come to 3 sqrt(45)

How about this? sqrt(5) + sqrt(20)

square root 5 = 1 *sqrt(5)

square root 20 = sqrt(2 * 2 * 5) = 2 sqrt(5)

x = sqrt(5)

y = 2*sqrt(5)

1sqrt(5) + 2 sqrt(5) = 3 sqrt(5) which is the same thing as sqrt(45)

It gets worse with part 2

sqrt (x + y) = sqrt(5 + 20) = sqrt(25) = 5