Evaluate square root of 343

Problem

√(,343)

Solution

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

2. Factor the number 343 into its prime components.

343=7×49

343=7×7×7

343=7

3. Rewrite the square root using the factored form to separate perfect squares.

√(,343)=√(,7×7)

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

√(,343)=√(,7)×√(,7)

5. Simplify the square root of the perfect square.

√(,343)=7√(,7)

Final Answer

√(,343)=7√(,7)

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