Originally Posted by
nycmath sqrt(7) - sqrt{8-2sqrt(7)} = 1
One of the expressions contains a radical within another radical.
sqrt{8-2sqrt(7)} = the square of 8 minus 2 times the square root of 7. All of this lies under one giant radical.
You are saying to move one expression to the right and then square both sides.
The original question is asking to show, to verify if both sides are equal. Does the left side equal 1?
Does sqrt(7) - sqrt{8-2sqrt(7)} equal one?
If I move one of the expressions to the right, it changes the value of 1 to (1-sqrt{7}). After squaring both sides, the two sides are not equal but this answer has nothing to do with the original request.
Does the left side containing a radical 7 minus a giant radical containing a radical within a radical equal 1?
Can you demonstrate just how "easy" this can be done without a calculator?