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Masharti muhimu Sura ya 09: Kuanzishwa kwa mizizi na Radicals

  • Page ID
    177868
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    Index
    Katika\(\sqrt[n]{a}\),\(n\) inaitwa index ya radical.
    Kama radicals
    Radicals na index sawa na radicand sawa huitwa kama radicals.
    Kama Mizizi ya mraba
    Mizizi ya mraba yenye radicand sawa huitwa kama mizizi ya mraba.
    Katika mizizi ya idadi
    Ikiwa\(b^n=a\), basi\(b\) ni na mizizi\(n\) ya\(a\).
    Mkuu katika mizizi
    Mzizi mkuu\(n\) wa\(a\) imeandikwa\(\sqrt[n]{a}\).
    radical equation
    Equation ambayo variable iko katika radicand ya mizizi ya mraba inaitwa equation radical.
    Mantiki watetezi
    • Kama\(\sqrt[n]{a}\) ni idadi halisi na\(n≥2\),\(𝑎^{\frac{1}{𝑛}}=\sqrt[n]{a}\).
    • Kwa integers yoyote chanya\(m\) na\(n\),\(a^{\frac{m}{n}}=(\sqrt[n]{a})^m\) na\(a^{\frac{m}{n}}=\sqrt[n]{a^m}\).
    Kutambua Denominator
    Mchakato wa kubadili sehemu na radical katika denominator kwa sehemu sawa ambayo denominator ni integer inaitwa rationalizing denominator.
    Mraba wa Idadi
    • Ikiwa\(n^2=m\), basi\(m\) ni mraba wa\(n\)
    Mizizi ya Mizizi ya mraba
    • Ikiwa\(m=n^2\), basi\(\sqrt{m}=n\). Tunasoma\(\sqrt{m}\) kama 'mizizi mraba ya\(m\). '
    Mizizi ya Mraba ya Idadi
    • Kama\(n^2=m\), basi\(n\) ni mizizi ya mraba ya\(m\)