Math Questions to review

Question 1

3√x^8 =

a) (x^2) 3√x^2
b) x^24
c) x^5
d) x^2
e) 24x

Answer 1

A - To simplify a cube root, find any cubes and remove them. x^3 appears twice within x^8, so you can pull out x^2. There will still be two x values under the root, so leave x^2 there: (x^2) 3√x^2

Basically, use the formula of x^8/3

Another way to look at this is to expand the expressions out. x^8 becomes (x)(x)(x)(x)(x)(x)(x)(x). As we are dealing with cubes, combine them into as many groups of “3”
((x)(x)(x)) ((x)(x)(x)) ((x)(x)) - or (x^3) (x^3) (x^2). Therefore, there are two cubes to remove from the cube root (each one becoming x) and x^2 is left behind. Outside of the radical, all roots are multiplied. Thus, (x^2) 3√x^2

Question 2

If 0

Answer 2

B - When a fraction between 0 and 1 is raised to a power greater than 1, the fraction becomes smaller. Likewise, when a root is taken of a fraction between 0 and 1, the fraction becomes larger. Thus, x^2

Question 3

(√27)(√3) =

a) 3√3
b) 9
c) 9√3
d) 18
e) 81

Answer 3

B - You can multiply roots together, even if the numbers under the roots and different. Thus, √27 * √3 = √27*3 = √81 = 9

Question 4

(3√x)^5 =

a) (x) (3√x^2)
b) x^15
c) x^2
d) 15√x
e) (x^2) (3√2x)

Answer 4

A - You can move the exponent under the roof, therefore (3√x)^5 = (3√x^5). That can then be converted into (x) (3√x^2) by pulling one set of x^3 out as x. Remaining under the root is x^2.

Question 5

Find the slope of the line that is perpendicular to the line 4x+5y=10

a) -4/5
b) -5/4
c) -1/4
d) 5/4
e) 4/5

Answer 5

D - Manipulate the equation so it is in y=mx+c form and find the negative reciprical of the “m”