Answer:
On a keyboard, we could type this as sqrt(3) + sqrt(5)
==============================================================
Explanation:
The given expression is considered a nested radical because one radical, the , is buried inside another radical.
Let's assume that nested radical is of the form where a & b are positive real numbers.
Set the given expression equal to and square both sides to see what happens. We'll do a bit of algebra to simplify and rearrange things a bit as well. See the steps below.
If we equate terms, we get this system of equations
Solve the first equation for 'a' to get a = 8-b
------------------------------
Let's plug a = 8-b into the second equation and solve for 'b'
If b = 3, then a = 8-b = 8-3 = 5
If b = 5, then a = 8-b = 8-5 = 3
We have this symmetry going on with 'a' and b. If one value is 3, then the other is 5, and vice versa. The order doesn't matter.
That means the equation
updates to
The order doesn't matter on the right side since we can add two numbers in any order.
---------
You can use your calculator to confirm the answer.
Note that
and
both result in the same decimal approximation to help show the two sides are equal.