(1+ square root of 5)(square root of 3-square root of 5)
To find the value of the expression, we can use the distributive property of multiplication.
(1 + sqrt(5))(sqrt(3) - sqrt(5))
First, distribute 1 to both terms inside the parentheses.
1 * sqrt(3) = sqrt(3)
1 * -sqrt(5) = -sqrt(5)
Next, distribute sqrt(5) to both terms inside the parentheses.
sqrt(5) * sqrt(3) = sqrt(15)
sqrt(5) * -sqrt(5) = -sqrt(25) = -5
Now, we can simplify the expression by combining like terms.
sqrt(3) - sqrt(5) + sqrt(15) - 5
So, the final value of the expression is sqrt(3) - sqrt(5) + sqrt(15) - 5.