Simplify square root of 8/9

Problem

√(,8/9)

Solution

1. Apply the quotient rule for radicals, which states that the square root of a fraction is the square root of the numerator divided by the square root of the denominator.

√(,8/9)=√(,8)/√(,9)

2. Simplify the denominator by calculating the square root of the perfect square 9

√(,8)/√(,9)=√(,8)/3

3. Factor the numerator to identify the largest perfect square factor of 8 which is 4

√(,8)/3=√(,4⋅2)/3

4. Apply the product rule for radicals to the numerator to separate the perfect square.

√(,4⋅2)/3=(√(,4)⋅√(,2))/3

5. Simplify the numerator by calculating the square root of 4

(2√(,2))/3

Final Answer

√(,8/9)=(2√(,2))/3

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