Simplify square root of 90

Problem

√(,90)

Solution

1. Identify the largest perfect square factor of the radicand 90

2. Factor the number 90 into a product of its largest perfect square factor and another integer.

90=9⋅10

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

√(,9⋅10)=√(,9)⋅√(,10)

4. Simplify the square root of the perfect square.

√(,9)=3

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

3⋅√(,10)

Final Answer

√(,90)=3√(,10)

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