Answer:
The expression 4sqrt(5) is equivalent
Explanation:
We can simplify the root by expresing the number in the sqrt in terms of numbers that have an integer sqrt root (such as 4, 9 etc) and following the rule :
sqrt(a*b) = sqrt (a)*sqrt(b)
To do that we do the prime factorization of 80 as follows:
80/2
40/2
20/2
10/2
5/2
Prime factorization : 2*2*2*2*5 = 4*4 *5
So we have:
sqrt(80)=sqrt(2*2*2*2*5)= sqrt(4*4*5)=sqrt(4)*sqrt(4)*sqrt(5)=2*2*sqrt(5)=4sqrt(5)