Simplify square root of 12/7

Problem

√(,12/7)

Solution

1. Apply the quotient rule for radicals to separate the numerator and the denominator.

√(,12/7)=√(,12)/√(,7)

2. Simplify the radical in the numerator by factoring out the largest perfect square.

√(,12)=√(,4⋅3)=2√(,3)

3. Substitute the simplified numerator back into the fraction.

(2√(,3))/√(,7)

4. Rationalize the denominator by multiplying both the numerator and the denominator by √(,7)

(2√(,3)⋅√(,7))/(√(,7)⋅√(,7))

5. Multiply the radicals in the numerator and simplify the denominator.

(2√(,21))/7

Final Answer

√(,12/7)=(2√(,21))/7

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