Question
Simplify. 10. \( \sqrt[3]{343} 7 \) 13. \( \sqrt[4]{2401} \) 16. \( \sqrt[3]{1331} \) 11
Ask by George Edwards. in the United States
Feb 27,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
\( \sqrt[3]{343} \times 7 = 49 \), \( \sqrt[4]{2401} = 7 \), \( \sqrt[3]{1331} = 11 \)
Solution
Calculate or simplify the expression \( \sqrt[3]{343} \times 7 \).
Calculate the value by following steps:
- step0: Calculate:
\(\sqrt[3]{343}\times 7\)
- step1: Simplify the root:
\(7\times 7\)
- step2: Multiply the numbers:
\(49\)
Calculate or simplify the expression \( \sqrt[4]{2401} \).
Calculate the value by following steps:
- step0: Calculate:
\(\sqrt[4]{2401}\)
- step1: Write in exponential form:
\(\sqrt[4]{7^{4}}\)
- step2: Simplify the root:
\(7\)
Calculate or simplify the expression \( \sqrt[3]{1331} \).
Calculate the value by following steps:
- step0: Calculate:
\(\sqrt[3]{1331}\)
- step1: Write in exponential form:
\(\sqrt[3]{11^{3}}\)
- step2: Simplify the root:
\(11\)
The simplified expressions are:
1. \( \sqrt[3]{343} \times 7 = 49 \)
2. \( \sqrt[4]{2401} = 7 \)
3. \( \sqrt[3]{1331} = 11 \)
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Simplify this solution Beyond the Answer
The cube root of 343 is 7, so when you multiply it by 7, you get 49. Thus, \( \sqrt[3]{343} \cdot 7 = 49 \). Next, the fourth root of 2401 is 7 as well, since \( 7^4 = 2401 \), so \( \sqrt[4]{2401} = 7 \). For the cube root of 1331, since \( 11^3 = 1331 \), we have \( \sqrt[3]{1331} = 11 \). So, putting it all together: 10. \( 49 \) 13. \( 7 \) 16. \( 11 \)
