Answer :

To simplify [tex]\(\sqrt[3]{343}\)[/tex], we need to find the number that, when multiplied by itself three times (cubed), equals 343.

Let's break it down:

1. Identify Perfect Cubes:
- Check if 343 is a perfect cube by considering smaller numbers that could be its cube root.
- Start with smaller numbers like 2, 3, 4, and continue upwards.

2. Test Number 7:
- Calculate [tex]\(7 \times 7 \times 7\)[/tex]:
- First, calculate [tex]\(7 \times 7 = 49\)[/tex].
- Then, calculate [tex]\(49 \times 7 = 343\)[/tex].

3. Conclusion:
- Since [tex]\(7^3 = 343\)[/tex], the cube root of 343 is 7.

Therefore, [tex]\(\sqrt[3]{343} = 7\)[/tex].

The simplified result is 7.

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