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Square Root and Cube Root Questions Answers Formulas, Tips and Tricks

  • 1. Square Root


    If \begin{aligned} a^2 = b \end{aligned}
    then we say that say that square root of b is a.
    and if we can write it as
    \begin{aligned} \sqrt{b} = a \end{aligned}

    for example \begin{aligned} \sqrt{9} = 3 \end{aligned}

  • 2. Cube Root


    The cube root of a number n is the number whose cube is n.
    We denote the cube root of n by
    \begin{aligned} \sqrt[3]{x} \\
    \text{We can write as,} \\

    \sqrt[3]{64} = \sqrt[3]{4*4*4} \\
    = 4
    \end{aligned}

  • 3. Important results for square root


    \begin{aligned}
    \sqrt{ab} = \sqrt{a}\times\sqrt{b} \\
    \sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}} = \frac{\sqrt{a}}{\sqrt{b}}\times\frac{\sqrt{b}}{\sqrt{b}} = \frac{\sqrt{ab}}{b}
    \end{aligned}