Question

Express -4√75 as a mixed radical in simplest form

Answer 1

You have the following expression:

`-4\sqrt[]{75}`

In order to express the previous number in its simplet radical form as a mixed radical, take into account that 75 can be written as follow:

75 = 25*3 = (5^2)*3

And

√(5^2*3) = 5√3

Hence, in the given expression, you have:

`-4\sqrt[]{75}=-4\sqrt[]{25\cdot3}=-4\sqrt[]{5^2\cdot3}=-4\cdot5\sqrt[]{3}=-20\sqrt[]{3}`

Hence, the result is:

-20√3