Perform the indicated operations:3√[48] + 7√[12] –√[75]?

Question

Perform the indicated operations:
3√[48] + 7√[12] –√[75]

Answer 1

The trick is to remember that you can pull out factors from the argument of the square root function. For example, sqrt(ab) can be rewritten as sqrt(a)*sqrt(b). That's very useful here, because each number having its square root taken is actually the product of 3 with a square number. So we can say 3*sqrt(48) + 7*sqrt(12) - sqrt(75) = 3*sqrt(16)*sqrt(3) + 7*sqrt(4)*sqrt(3) - sqrt(25)*sqrt(3) = 3*4*sqrt(3) + 7*2*sqrt(3) - 5*sqrt(3) = 12*sqrt(3) + 14*sqrt(3) - 5*sqrt(3) = 21*sqrt(3).

Answer 2

3√[48] + 7√[12] –√[75]
=3√[2*2*2*2*3] + 7√[3*2*2] –√[3*5*5]
=12√[3] + 14√[3] – 5√[3]
=21√[3]

Answer 3

=12sqrt(3)+14sqrt(3)-5sqrt(3)
=21sqrt(3)

Answer 4

36.37