sqrt(175) / 35

sqrt(5*35) / 35

sqrt(7) / 7

1 / sqrt(7)

sqrt(35) / 35

4throot(162x^4) / (3x)

4throot(54x^4) / (3x)

4throot(54x^3) / (3x)

4throot(18x^2) / (3x)

4throot(6x) / (3x)

3 Read all choices carefully, since several answers look correct but are not: Simplify cuberoot(3(x^2)y) / cuberoot(5xy^2), rationalizing the denominator to put your answer in "simplest form." Assume x and y are not 0. Your answer could be written as:

cuberoot(3x/(5y))

cuberoot(75xy^2)/(5y)

cuberoot(3x)/cuberoot(5y)

cuberoot(15(x^2)(y^2)) / (5y^2)

cuberoot(15xy) / (5y)

## 1 Resposta

Hi Rr L.,

This exercise is building on your previously-learned (?) expression manipulation skills. Here, you are asked to make sure that your final answer has no "rooted" expressions in the denominator (there can, however, be rooted expressions in the numerator).

(A) So if you see, for example, a √(35) in the denominator, multiply both the numerator and the denominator by √(35). Why?

(1) because doing that will convert the denominator into a non-rooted number, and

(2) because if you multiply the numerator by something, you must multiply the denominator by that same thing, in order to keep the value of the expression unchanged. Note that the value of the expression is not the same as "the way the expression is written"!

So, once you have done that:

(B) Simplify all the terms in the numerator and denominator, as much as possible. For any "rooted" factors, remember that √A*√B = √(AB). That is to say, that multiplication distributes under exponentiation (and roots are, after all, just fractional exponents; √a = a1/2 , 4th root of (a) = a1/4 , and so on).

(C) In the first problem, it is then possible to simplify further, by factoring out a perfect square, since the numerator is √(5*7*5), so that will simplify to 5*√7 , right? And also √35*√35 = 35, don't even bother to do a multiplication, a (square root of anything) squared is just the original anything.