(1+ square root of 5)(square root of 3-square root of 5)
To simplify the expression (1 + √5)(√3 - √5), we can use a property of radicals that states √a * √b = √(a * b).
So, let's apply this property to simplify the expression:
(1 + √5)(√3 - √5)
= 1√3 - 1√5 + √5√3 - √5√5 (using the distributive property)
= √3 - √5 + √5√3 - 5 (since √5√5 simplifies to 5)
= √3 - √5 + √(5 * 3) - 5 (using the property √a * √b = √(a * b))
= √3 - √5 + √15 - 5 (simplifying the square root of 15)
This is the simplified form of the expression (1 + √5)(√3 - √5).