Question

Simplify

Radical 28/75

Answer 1

This?

\( \sqrt{\dfrac{28}{75} }\)

Answer 2

Yeah

Answer 3

Let's look at the prime factors of 28 and 75:

\( \sqrt{\dfrac{2 \times 2 \times 7}{3 \times 5 \times 5} }\)

This allows you to simplify this a bit before rationalizing.

Answer 4

Yeah

Answer 5

\( =\sqrt{ \dfrac{4}{25}} \sqrt{\dfrac{7}{3} }\)

\(= \dfrac{2}{5} \sqrt{\dfrac{7}{3} }\)

\(= \dfrac{2}{5} \dfrac{\sqrt{7}}{\sqrt{3}}\)

Answer 6

There is still a sqrt(3) in the denominator. Now we need to rationalize the denominator.

Answer 7

\(= \dfrac{2}{5} \dfrac{\sqrt{7}}{\sqrt{3}} \dfrac{\sqrt{3}}{\sqrt{3}}\)

\(= \dfrac{2}{5} \dfrac{\sqrt{21}}{3} \)

\(= \dfrac{2\sqrt{21} }{15} \)