Question

What is the simplest form of the expression?

√20 + √45 - √5
A. 5√5
B. 6√5
C. 4√5
D. 13√5

Answer 1

Simplify 20−−√20 to 25√25
25√+45−−√−5√
25+45−5

2 Simplify 45−−√45 to 35√35
25√+35√−5√
25+35−5

3 Simplify
45√

Answer 2

The answer is C. 4√5

To calculate this, we must find the greatest common divisor of these 3 numbers √20,√45, and √5.
The greatest common divisor is √5:

`√(20) = √(5*4) = √(5) * √(4) = √(5) *2= 2√(5)`

`√(45) = √(5*9) = √(5) * √(9)=√(5)*3 = 3√(5)`

Therefore,

`√(20) + √(45)- √(5)=2 √(5) +3√(5)-1√(5)=√(5)(2+3-1)=4√(5)`