I bet your calculator knows. Are you allowed to use it?
Spoiler:
There is no need for any squaring......
and
Then use the property of surd conjugates
Since 7-3=6-2, then (surd)(surd conjugate) is equal for both.
Hence, since
A more general way to look at this.....
For any positive difference "k" and any positive increment "w"
Yet another general way to consider it is as follows.....
Generally as the numbers increase with a common difference, the difference between their square roots keeps decreasing,
since , defined for x>4, becomes insignificantly small as x increases without bound,
while x-(x-4) is always 4.
This means as "n" keeps increasing.
You can use calculus to show that
is a decreasing function as x increases.
Therefore the derivative is negative, so the function is a decreasing function.
Therefore
You could also examine the function
which is defined for x positive.