β(59,049) - What Is the cubed root of 59,049 ?
This Is the same as (59,049)β
Step by Step solution
We attempt To simplify the cubed root Of 59,049
Step 1: Factor 59,049
59,049 can be written as a product of its prime factors in the following way: 59,049 = 310
The factors were found in the following order:
59,049 = 3 Γ 19,683
19,683 = 3 Γ 6,561
6,561 = 3 Γ 2,187
2,187 = 3 Γ 729
729 = 3 Γ 243
243 = 3 Γ 81
81 = 3 Γ 27
27 = 3 Γ 9
9 = 3 Γ 3
Step 2: Rewrite β(59,049)
β(59,049) =
β(310) =
β(310)
β(310) = β(310)
Step 3: Simplify β(310)
Step 3.1 Rewrite β(310)
β(310) = β(33) Γ β(33) Γ β(33) Γ β(31)
Step 4: Simplify β(310)
Step 4.1 Simplify β(33)
Using the exponent "product rule", we know that
β(33) = ((3)3)β
= 3(3Γβ
) = 31 = 3
Step 4.2 Simplify β(33)
Using the exponent "product rule", we know that
β(33) = ((3)3)β
= 3(3Γβ
) = 31 = 3
Step 4.3 Simplify β(33)
Using the exponent "product rule", we know that
β(33) = ((3)3)β
= 3(3Γβ
) = 31 = 3
Step 4.4 Simplify β(31)
As per raising to the power of one: 3^1 = 3
So, we can rewrite β(31) = β(3) = 1.44224957030741
Final Result
β(59,049) = 3 Γ 3 Γ 3 Γ 1.44224957030741
One real solution was found
38.9407383983001
Theory And Definitions
Product with same base When multiplying like bases, keep the base the same and add the exponents. In General (xm)Γ(xn) = x(m+n) and as an example (x2)Γ(x3) = x(2+3) = x5
The product Of roots rule states that the root of a product Is equal to the root of each factor of the product multiplied together.
Power of one rule states that any number raised to the power of one is the original number itself. In General: x1=x and as an example: 51=5
Step-by-step explanation:
