Evaluate square root of 294

Problem

√(,294)

Solution

1. Identify the prime factors of the number 294 to see if it contains any perfect square factors.

2. Divide by the smallest prime number, 2 which gives 294=2×147

3. Divide 147 by its smallest prime factor, 3 which gives 147=3×49

4. Recognize that 49 is a perfect square, as 49=7×7

5. Rewrite the original expression using these factors:

√(,294)=√(,2×3×7)

6. Apply the product property of radicals √(,a×b)=√(,a)×√(,b) to simplify the expression.

√(,294)=√(,7)×√(,2×3)

7. Simplify the square root of the perfect square and multiply the remaining factors under the radical.

√(,294)=7√(,6)

Final Answer

√(,294)=7√(,6)

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