Here we will explain how to simplify the cube root of 45 (∛45). We start by labeling the parts of ∛45 so it is easy to follow along:
∛45 = 1∛45 = c∛r
c = coefficient of the radical
∛ = radical
r = radicand
The cube root of 45 in its simplest form means that you want the radicand to be as small as possible and the coefficient of the radical to be as large as possible.
To simplify the cube root of 45, we first find the greatest perfect cube from the list of factors of 45. The factors of 45 are 1, 3, 5, 9, 15, and 45.
Any number multiplied by itself three times will make a perfect cube. The greatest perfect cube from the list of factors above is 1 (1 times 1 times 1 equals 1).
To find the simplified radicand (r) in the cube root of 45, we divide 45 by 1, which gives us 45.
To find the simplified coefficient of the radical (c) in the cube root of 45, we take the cube root of 1, which gives us 1.
That is how you simplify the cube root of 45. Therefore, the cube root of 45 in its simplest radical form is as follows:
∛45 = ∛45
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