Calculate the square root of 68

Problem

√(,68)

Solution

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

2. Factor the number 68 into a product of a perfect square and another integer.

68=4×17

3. Apply the product rule for radicals, which states √(,a×b)=√(,a)×√(,b)

√(,68)=√(,4×17)

√(,68)=√(,4)×√(,17)

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

√(,4)=2

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

√(,68)=2√(,17)

Final Answer

√(,68)=2√(,17)

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