Evaluate cube root of 343

Problem

√(3,343)

Solution

1. Identify the number under the radical, which is 343 and determine if it is a perfect cube.

2. Factor the number into its prime components to see if it can be expressed as a power of 3

3. Observe that 343 is not divisible by 2 (it is odd), 3 (sum of digits is 10, or 5 (does not end in 0 or 5.

4. Test the next prime number, 7 by dividing: 343÷7=49

5. Continue factoring 49 to find that 49=7×7

6. Rewrite the original number as a power of 7 343=7×7×7=7

7. Apply the property of radicals √(n,xn)=x to simplify the expression.

Final Answer

√(3,343)=7

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