Question

A rectangle has a length of the cube root of 81 inches and a width of 3 to the 2 over 3 power inches. Find the area of the rectangle.

3 to the 2 over 3 power inches squared
3 to the 8 over 3 power inches squared
9 inches squared
9 to the 2 over 3 power inches squared

Answer 1

Let's find the length, what's the cube root of 81?

Answer 2

um dont I multiply 81 by 3? to find it

Answer 3

No
Cuberoot(3x3x3x3)
Cuberoot(3^3 x 3)=?????

Answer 4

So I multiply 81 with 3x3x3x3

Answer 5

No 3x3x3x3 =81
I just factored the number so you can se tha it's formed by 3x3x3x3
Now the cube root will eliminate 3 of these 3 of the the root,
So you get
3cbrt(3)

Answer 6

Now, the width
A number raised to a fraction can be transformed into a root like this
A^b/c
Croot(a^b)
So 2 to the2/3
Will be cube root of 2^2
How much is
Cube root of 2^2?

Answer 7

4?

Answer 8

So we get cube root of four.
Now the area of a rectangle is
Width times length
How much is
Cuberoot of 4 x 3x cuberoot of 3????

Answer 9

36?

Answer 10

@gaos