Evaluate square root of 140

Problem

√(,140)

Solution

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

140=2×70

140=2×2×35

140=2×5×7

2. Rewrite the radical expression using the identified perfect square factor.

√(,140)=√(,4×35)

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

√(,140)=√(,4)×√(,35)

4. Simplify the square root of the perfect square.

√(,4)=2

5. Combine the terms to reach the simplest radical form.

√(,140)=2√(,35)

Final Answer

√(,140)=2√(,35)

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