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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
    • 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
    • If \(n^2=m\), then \(m\) is the square of \(n\)
    Square Root Notation
    • If \(m=n^2\), then \(\sqrt{m}=n\). We read \(\sqrt{m}\) as ‘the square root of \(m\).’
    Square Root of a Number
    • If \(n^2=m\), then \(n\) is a square root of \(m\)
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