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A root is a mathematical operation that determines the value which, when multiplied by itself a specified number of times, equals the given number. The most common root is the square root, denoted by \( \sqrt{a} \), which represents the second root of a number. In general, the \( n \)-th root is expressed as \( \sqrt[n]{a} \), which finds a number \( x \) such that: \( x^n = a \).
Solution:
Compute:
\( x = \sqrt{16} = 4 \)
Conclusion: The square root of 16 is 4.
Solution:
Compute:
\( x = \sqrt[3]{27} = 3 \)
Conclusion: The cube root of 27 is 3.
Solution:
Compute:
\( x = \sqrt[4]{81} = 3 \)
Conclusion: The fourth root of 81 is 3.
Solution:
Compute:
\( x = \sqrt[3]{1000} = 10 \)
Conclusion: The cube root of 1000 is 10.