Calculate the square root of 147

Problem

√(,147)

Solution

1. Identify the number inside the radical and look for perfect square factors.

2. Factor the number 147 by checking for divisibility. Since the sum of the digits 1 + 4 + 7 = 12$ is divisible by 3, the number is divisible by 3.

3. Divide 147 by 3 to find the other factor.

147=3×49

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

√(,147)=√(,49×3)

√(,147)=√(,49)×√(,3)

5. Simplify the square root of the perfect square 49.

√(,49)=7

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

√(,147)=7√(,3)

Final Answer

√(,147)=7√(,3)

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