Köklü Sayılarda Dört İşlem

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Köklü sayılarda dört işlem nasıl yapılır? Köklü ifadelerde toplama, çıkarma, çarpma ve bölme kuralları, örnekler.

KÖKLÜ İFADELER

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\displaystyle {{a}^{n/m}}=\sqrt[m]{{{a}^{n}}} ifadesinde kökün derecesi m’dir.

\displaystyle \sqrt[m]{a}=x\Rightarrow {{x}^{m}}=a

TOPLAMA-ÇIKARMA

\displaystyle *a\sqrt[n]{x}-b\sqrt[n]{x}+c\sqrt[n]{x}=\left( a-b+c \right)\sqrt[n]{x}

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\displaystyle \sqrt{a}+\sqrt{b}\ne \sqrt{a+b}

Örnek;

\displaystyle 4\sqrt[3]{2}+2\sqrt[3]{2}-3\sqrt[3]{2}=\left( 4+2-3 \right)\sqrt[3]{2}=3\sqrt[3]{2}

ÇARPMA

\displaystyle \sqrt[n]{a}.\sqrt[n]{b}=\sqrt[n]{a.b}

Örnek;

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\displaystyle \sqrt[3]{2}.\sqrt[3]{4}=\sqrt[3]{2.8}=\sqrt[3]{16}

BÖLME;

\displaystyle \frac{\sqrt[n]{a}}{\sqrt[n]{b}}=\sqrt[n]{\frac{a}{b}}

Örnek;

\displaystyle \frac{\sqrt[3]{2}}{\sqrt[3]{3}}=\sqrt[3]{\frac{2}{3}}

PAYDAYI RASYONEL YAPMA

\displaystyle *\frac{a}{\sqrt{b}}=\frac{a.\sqrt{b}}{\sqrt{b}.\sqrt{b}}=\frac{a\sqrt{b}}{b}

\displaystyle *\frac{a}{\sqrt[n]{b}}=\frac{a.\sqrt[n]{{{b}^{n-1}}}}{\sqrt[n]{b}.\sqrt[n]{{{b}^{n-1}}}}=\frac{a.\sqrt[n]{{{b}^{n-1}}}}{b}

\displaystyle *\frac{a}{\sqrt{b}+\sqrt{c}}=\frac{a.\left( \sqrt{b}-\sqrt{c} \right)}{\left( \sqrt{b}+\sqrt{c} \right)\left( \sqrt{b}-\sqrt{c} \right)}=\frac{a.\left( \sqrt{b}-\sqrt{c} \right)}{b-c}

\displaystyle *\frac{a}{\sqrt[3]{b}+\sqrt[3]{c}}=\frac{a.\left( \sqrt[3]{{{b}^{2}}}-\sqrt[3]{bc}+\sqrt[3]{{{c}^{2}}} \right)}{\left( \sqrt[3]{b}+\sqrt[3]{c} \right)\left( \sqrt[3]{{{b}^{2}}}-\sqrt[3]{bc}+\sqrt[3]{{{c}^{2}}} \right)}=\frac{a\left( \sqrt[3]{{{b}^{2}}}-\sqrt[3]{bc}+\sqrt[3]{{{c}^{2}}} \right)}{b+c}

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