Are these two quantities alike or not alike?
Does one side agree with the other?

sqrt(7) - sqrt{8-2sqrt(7)} = 1

transfer 1 to the left and the sqrt{8-...) to the right and then rise to power 2 and see what you get......it is easy
you can do it yourself.

sqrt(7) - sqrt{8-2sqrt(7)} = 1

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.

Can you demonstrate just how "easy" this can be done without a calculator?

Originally Posted by nycmath
sqrt(7) - sqrt{8-2sqrt(7)} = 1

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.

Can you demonstrate just how "easy" this can be done without a calculator?
As I mentioned in the other thread with a similar problem, you want to get rid of that double square root. So isolate it:
$\displaystyle \sqrt{7} - \sqrt{8-2\sqrt{7}} = 1$

$\displaystyle \sqrt{7} - 1 = \sqrt{8-2\sqrt{7}}$

Now square both sides and see what happens.

-Dan

PS Feel free to visit our LaTeX forum. It only looks like it's hard to use but you can actually pick it up fairly quickly.