Question

Find the decimal expansion of root 125

Answer 1

$\textbf{Given:}$

$\mathsf{\sqrt{125}}$

$\textbf{To find:}$

$\textsf{Decimal expansion of}\;\mathsf{\sqrt{125}}$

$\textbf{Solution:}$

$\textsf{Consider,}$

$\mathsf{\sqrt{125}}$

$\mathsf{=\sqrt{25{\times}5}}$

$\mathsf{Using,}$

$\boxed{\mathsf{\sqrt{a{\times}b}=\sqrt{a}{\times}\sqrt{b}}}$

$\mathsf{=\sqrt{25}{\times}\sqrt{5}}$

$\mathsf{=5{\times}\sqrt{5}}$

$\mathsf{=5{\times}2.236}$

$\mathsf{=11.18}$

$\implies\boxed{\mathsf{\sqrt{125}=11.18}}$

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