To simplify the expression E = √(3+√5)² - √5, we can start by expanding the square inside the square root:

E = √((3+√5)(3+√5)) - √5

Next, we can simplify the expression inside the first square root by using the distributive property:

E = √(9 + 3√5 + 3√5 + 5) - √5

Simplifying further, we combine like terms:

E = √(14 + 6√5) - √5

Now, we can subtract the square root terms:

E = √(14 + 6√5) - √5

To simplify this expression further, we can rationalize the denominator by multiplying both the numerator and denominator by the conjugate of the denominator:

E = (√(14 + 6√5) - √5) * (√(14 + 6√5) + √5) / (√(14 + 6√5) + √5)

Using the difference of squares formula, the denominator becomes:

E = (√(14 + 6√5) - √5) * (√(14 + 6√5) + √5) / (14 + 6√5 - 5)

Simplifying the denominator:

E = (√(14 + 6√5) - √5) * (√(14 + 6√5) + √5) / (14 + 6√5 - 5)
= (√(14 + 6√5) - √5) * (√(14 + 6√5) + √5) / (9 + 6√5)

Now, we can simplify the numerator by using the difference of squares formula:

E = ((14 + 6√5) - 5) / (9 + 6√5)
= (9 + 6√5) / (9 + 6√5)

Finally, we can cancel out the common terms in the numerator and denominator:

E = 1

Therefore, E = 1.