Evaluate square root of 24502

Problem

√(,24⋅50⋅2)

Solution

1. Group the numbers inside the square root to find easy products.

√(,24⋅(50⋅2))

2. Multiply the terms inside the parentheses.

√(,24⋅100)

3. Apply the product property of square roots, which states √(,a⋅b)=√(,a)⋅√(,b)

√(,24)⋅√(,100)

4. Evaluate the square root of the perfect square.

√(,24)⋅10

5. Factor the remaining radicand to find any additional perfect squares.

√(,4⋅6)⋅10

6. Simplify the square root of the factor.

2√(,6)⋅10

7. Multiply the coefficients to reach the final result.

20√(,6)

Final Answer

√(,24⋅50⋅2)=20√(,6)

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