Calculate the square root of 252

Problem

√(,252)

Solution

1. Identify the number under the radical and look for its prime factors.

2. Factor the number 252 by dividing by the smallest prime numbers.

252=2⋅126

126=2⋅63

63=3⋅21

21=3⋅7

3. Group the prime factors into pairs of squares.

252=2⋅3⋅7

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

√(,252)=√(,2⋅3⋅7)

5. Simplify the radical by taking the square root of the squared terms.

√(,252)=2⋅3⋅√(,7)

6. Multiply the coefficients outside the radical.

2⋅3=6

Final Answer

√(,252)=6√(,7)

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