Which expression is equivalent to sqrt 80

The expression 4sqrt (5) is equivalent

Step-by-step 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)