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)

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step-by-step explanation:

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