Evaluate cube root of 81

Problem

√(3,81)

Solution

1. Identify the number under the radical and express it as a product of its prime factors.

√(3,81)=√(3,3⋅3⋅3⋅3)

2. Rewrite the expression using exponents to group the factors into a power of three.

√(3,81)=√(3,3⋅3)

3. Apply the property of radicals where √(n,a⋅b)=√(n,a)⋅√(n,b) to separate the terms.

√(3,81)=√(3,3)⋅√(3,3)

4. Simplify the cube root of the cubed term, noting that √(3,3)=3

√(3,81)=3⋅√(3,3)

Final Answer

√(3,81)=3√(3,3)

Want more problems? Check here!