Question

`(42)/( √(28) ) + (60)/(45) - 2 √(20) + 2√(175)`
​

Answer 1

4/3−4√5+13√7

Explanation:

So for whatever reason we don't like it when the radical is in the denominator so we're going to do a process called rationalization and get rid of it. We do this by multiplying both the numerator and denominator by the radical

So for the first part we multiply the numerator and denominator by
`√(28)` which gives us
`(42√(28) )/(28)` we can then factor the 28 into sqrt(7,2,2) which simplifies to
`42*2√(7)`/28 So then we can simplify this and get
`3√(7)` We then can simplify the rest of these radicals and get
`2√(20)=2√(2*2*5)=4√(5)` and
`2√(175)= 2√(5*5*7)=2*5√(7)` This means that so far we have the following:
`3√(7)+ (60)/(45)-4√(5) +10√(7)` We can add the like terms and simplify the fraction and get 4/3−4√5+13√7