How do you simplify square roots? Like how can you get sqrt28 to be 2sqrt7?

Answer 1

a number like √28 can be changed to a mixed radical by looking for factors of 28 which are perfect squares

perfect squares are 4,9,16,25,36,49,64,...

since 28 = 4x7
√28 = √4 x √7
= 2√7

splitting 28 up into factors that do not contain a perfect square, does us no good.
e.g.
√28 = √2 x √14 , nothing gained here.

If a number does not contain a perfect square number it cannot be changed into a mixed radical

Answer 2

Review examples 2, 3, and 4 in section 8.4 of the text. How does the author determine what the first equation should be? What about the second equation? How are these examples similar? How are they different? Find a problem in the text that is similar to examples 2, 3, and 4. Post the problem for your classmates to solve.