Calculate the square root of 175

Problem

√(,175)

Solution

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

2. Factor the number 175 by finding its divisors.

175=25×7

3. Rewrite the expression using the factors found.

√(,175)=√(,25×7)

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

√(,25×7)=√(,25)×√(,7)

5. Simplify the square root of the perfect square 25

√(,25)=5

6. Combine the results to get the simplified radical form.

5×√(,7)=5√(,7)

Final Answer

√(,175)=5√(,7)

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