What is the simplest form of the radical expression?
sqft2+sqft5/sqft2-sqft5
To simplify the expression (sqrt(2) + sqrt(5))/(sqrt(2) - sqrt(5)), you need to rationalize the denominator. This can be done by multiplying both the numerator and denominator by the conjugate of the denominator, which is sqrt(2) + sqrt(5).
This results in:
((sqrt(2) + sqrt(5))/(sqrt(2) - sqrt(5))) * ((sqrt(2) + sqrt(5))/(sqrt(2) + sqrt(5)))
Expanding the numerator using the distributive property:
(sqrt(2) + sqrt(5))^2 = 2 + 2 sqrt(2)sqrt(5) + 5
= 7 + 2 sqrt(10)
Expanding the denominator:
(sqrt(2) - sqrt(5))(sqrt(2) + sqrt(5)) = 2 - 5
= -3
Therefore, the simplified form of the expression is (7 + 2 sqrt(10))/-3.