Question

rationalizing factor of root 180​

Answer 1

$\underline{\textsf{Given:}}$

$\mathsf{\sqrt{180}}$

$\underline{\textsf{To find:}}$

$\textsf{The rationalizing factor of}$

$\mathsf{\sqrt{180}}$

$\underline{\textsf{Solution:}}$

$\textsf{Consider,}$

$\mathsf{\sqrt{180}}$

$\mathsf{=\sqrt{36{\times}5}}$

$\mathsf{=\sqrt{36}{\times}\sqrt{5}}$

$\implies\mathsf{\sqrt{180}=6\sqrt{5}}$

$\textsf{when multiplying by}\;\mathsf{\sqrt{5}}$

$\mathsf{\sqrt{180}{\times}\sqrt{5}=6\sqrt{5}{\times}\sqrt{5}}$

$\mathsf{\sqrt{180}{\times}\sqrt{5}=6{\times}5=30}$

$\textsf{which is rational}$

$\therefore\textsf{Rationalizing factor of}\;\mathsf{\sqrt{180}}$

$\textsf{is}\;\mathsf{\sqrt{5}}$

Answer 2

$Given \: number \: \sqrt{180}$

$Resolving \: 180 \:into \: product$

$of \: prime \: factors , we \:get$

2 | 180

________

2 | 90

________

3 | 45

________

3 | 15

________

**** 5

180 = 2×2×3×3×5

$\sqrt{180} = \sqrt{2^{2} \times 3^{2} \times 5 }$

$= 2\times 3 \times \sqrt{5}$

$= 6\sqrt{5}$

$\red{ Rationalising \:factor \: of \: \sqrt{180}\: is }$

$\green {= \sqrt{5}}$

$\underline{ \pink{ Explanation :}}$

$\sqrt{180} \times \sqrt{5}$

$= 6\sqrt{5} \times \sqrt{5}$

$= 6 \times 5$

$= 30 \: \blue {( Rational \: number ) }$

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