Evaluate fourth root of 40 fourth root of 250

Problem

√(4,40)√(4,250)

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.

40⋅250=10000

3. Rewrite the radicand as a power of 10 to simplify the expression.

10000=10

4. Simplify the radical by applying the rule that the nth root of a number raised to the nth power is the number itself.

√(4,10)=10

Final Answer

√(4,40)√(4,250)=10

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