Question

How do you simplify the square root of 28 times the square root of 14?

Answer 1

`14sqrt(2)`

Explanation:

You can rewrite each radicand as a product of its prime factors:
`sqrt(28) * sqrt(14) = sqrt(2*2*7) * sqrt(2*7)`

You can then separate each factor into individual radicands:
`sqrt(2*2*7) * sqrt(2*7) = sqrt(2) * sqrt(2) * sqrt(2) * sqrt(7) * sqrt(7)`

Next multiply the square roots that have a matching pair:
`sqrt(2) * sqrt(2) * sqrt(2) * sqrt(7) * sqrt(7) = 2 * sqrt(2) * 7`

Finally, simplify:
`2 * sqrt(2) * 7 = 14sqrt(2)`