Math, asked by pravin86, 1 year ago

Find the values of √4225. Using this find the value of √42.25 + √0.4225 .

Answers

Answered by MaheswariS
4

\underline{\textbf{Given:}}

\mathsf{\sqrt{42.25}+\sqrt{0.4225}}

\underline{\textbf{To find:}}

\mathsf{(i)\;The\;value\;of\;\sqrt{4225}}

\mathsf{(ii)\;The\;value\;of\;\sqrt{42.25}+\sqrt{0.4225}}

\underline{\textbf{Solution:}}

\textsf{By Prime factorization,}

\mathsf{4225=13{\times}13{\times}5{\times}5}

\mathsf{\sqrt{4225}=13{\times}5}

\implies\mathsf{\sqrt{4225}=65}

\mathsf{Consider,}

\mathsf{\sqrt{42.25}+\sqrt{0.4225}}

\mathsf{=\sqrt{\dfrac{4225}{100}}+\sqrt{\dfrac{4225}{10000}}}

\mathsf{=\dfrac{\sqrt{4225}}{\sqrt{100}}}+\dfrac{\sqrt{4225}}{\sqrt{10000}}}

\mathsf{=\dfrac{65}{10}+\dfrac{65}{100}}

\mathsf{=6.5+0.65}

\mathsf{=7.15}

\implies\boxed{\bf\sqrt{42.25}+\sqrt{0.4225}=7.15}

#SPJ3

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