Calculate the square root of 160

Problem

√(,160)

Solution

1. Identify the number under the radical and look for its largest perfect square factor.

2. Factor the number 160 into a product of a perfect square and another integer.

160=16⋅10

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

√(,160)=√(,16⋅10)

√(,160)=√(,16)⋅√(,10)

4. Simplify the square root of the perfect square factor.

√(,16)=4

5. Combine the results to write the expression in simplest radical form.

√(,160)=4√(,10)

Final Answer

√(,160)=4√(,10)

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