Key Terms Chapter 09: Roots and Radicals Introduction
- Page ID
- 101930
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- Index
- In \(\sqrt[n]{a}\), \(n\) is called the index of the radical.
- Like Radicals
- Radicals with the same index and same radicand are called like radicals.
- Like Square Roots
- Square roots with the same radicand are called like square roots.
- nth root of a number
- If \(b^n=a\), then \(b\) is an \(n\)th root of \(a\).
- Principal nth Root
- The principal \(n\)th root of \(a\) is written \(\sqrt[n]{a}\).
- Radical Equation
- An equation in which the variable is in the radicand of a square root is called a radical equation
- Rational Exponents
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- If \(\sqrt[n]{a}\) is a real number and \(n≥2\), \(𝑎^{\frac{1}{𝑛}}=\sqrt[n]{a}\).
- For any positive integers \(m\) and \(n\), \(a^{\frac{m}{n}}=(\sqrt[n]{a})^m\) and \(a^{\frac{m}{n}}=\sqrt[n]{a^m}\).
- Rationalizing the Denominator
- The process of converting a fraction with a radical in the denominator to an equivalent fraction whose denominator is an integer is called rationalizing the denominator.
- Square of a Number
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- If \(n^2=m\), then \(m\) is the square of \(n\)
- Square Root Notation
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- If \(m=n^2\), then \(\sqrt{m}=n\). We read \(\sqrt{m}\) as ‘the square root of \(m\).’
- Square Root of a Number
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- If \(n^2=m\), then \(n\) is a square root of \(m\)