Evaluate fourth root of 24 fourth root of 54

Problem

√(4,24)⋅√(4,54)

Solution

1. Apply the product property of radicals to combine the two fourth roots into a single radical expression.

√(4,a)⋅√(4,b)=√(4,a⋅b)

2. Multiply the radicands inside the fourth root.

√(4,24⋅54)

3. Find the product of the two numbers.

24⋅54=1296

4. Rewrite the expression with the calculated product.

√(4,1296)

5. Determine the fourth root by identifying which number raised to the power of 4 equals 1296.

6=1296

Final Answer

√(4,24)⋅√(4,54)=6

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