Question

( √(3 + √5) - √(3 - √5) )²

Answer 1

$(\sqrt{3-3+\sqrt{5}+\sqrt{5} } )^{2} =(2\sqrt{5}) ^{2} =4*5=20$

Answer 2

To simplify the expression ( √(3 + √5) - √(3 - √5) )², we'll first need to apply the difference of squares formula. The difference of squares formula states that:

(a - b)² = a² - 2ab + b²

In this case, a is √(3 + √5) and b is √(3 - √5).

Let's proceed with the simplification step by step:

Step 1: Calculate (a - b) √(3 + √5) - √(3 - √5)

Step 2: Square the result from Step 1 (√(3 + √5) - √(3 - √5))² = (√(3 + √5) - √(3 - √5)) * (√(3 + √5) - √(3 - √5))

Step 3: Apply the difference of squares formula (a² - 2ab + b²) = (√(3 + √5))² - 2 * (√(3 + √5)) * (√(3 - √5)) + (√(3 - √5))²

Step 4: Simplify the individual terms = (3 + √5) - 2 * √((3 + √5) * (3 - √5)) + (3 - √5)

Step 5: Simplify the middle term under the square root Notice that (3 + √5) * (3 - √5) is a difference of squares, which simplifies to (3)² - (√5)² = 9 - 5 = 4.

= (3 + √5) - 2 * √4 + (3 - √5)

Step 6: Simplify further = 3 + √5 - 2 * 2 + 3 - √5

Step 7: Combine like terms = 3 - 4 + √5 + √5

Step 8: Simplify further = -1 + 2√5

So, the simplified expression is -1 + 2√5.