Calculate the square root of 52

Problem

√(,52)

Solution

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

2. Factor the number 52 into a product of a perfect square and another integer.

52=4×13

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

√(,52)=√(,4×13)

√(,52)=√(,4)×√(,13)

4. Simplify the square root of the perfect square 4

√(,4)=2

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

√(,52)=2√(,13)

Final Answer

√(,52)=2√(,13)

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