Evaluate -6 fourth root of 486

Problem

−6√(4,486)

Solution

1. Identify the radicand and the index of the root. The radicand is 486 and the index is 4

2. Find the prime factorization of 486 to identify perfect fourth powers.

486=2⋅243

486=2⋅3

3. Rewrite the radicand as a product of a perfect fourth power and a remaining factor.

486=3⋅(2⋅3)

486=81⋅6

4. Apply the product property of radicals to separate the perfect fourth power.

−6√(4,81⋅6)=−6√(4,81)⋅√(4,6)

5. Simplify the fourth root of the perfect power.

√(4,81)=3

6. Multiply the resulting integer by the coefficient outside the radical.

−6⋅3⋅√(4,6)=−18√(4,6)

Final Answer

−6√(4,486)=−18√(4,6)

Want more problems? Check here!