Question

Solve these questions. I will Mark me Brainliest ​​

Answer 1

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✺Question

$\rm{\Large{ \rightarrow \: 3 \sqrt{147} - \frac{7}{3} \sqrt{ \frac{1}{3} } + 7\sqrt{ \frac{1}{3} }}}$

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✺Explanation of Q.

The above equation contains three terms with square roots but they are not in simplied terms. So first we need to simplify them, to reduce calculation.

I am simplying the terms individually. Let,

$\oplus{\large{ \: \: \boxed{ \rm{ \red{3 \sqrt{147} }}}} - \boxed{ \rm{ \red{\frac{7}{3} \sqrt{ \frac{1}{3} } }}} \: + \: \boxed{ \rm{ \red{7 \sqrt{ \frac{1}{3} } }}}} \\ \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \downarrow \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \downarrow \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \downarrow \\ \rm{\large{ \bold{ \: \: \: \: \: \: \: \: \: \: \: \: A \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: B \: \: \: \: \: \: \: \: \: \: \: \: \: \: C}}}$

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✺Simplying Each term = A, B, C

$\huge{ \rm{ \underline{ \underline{ \green{A}}}}} \\ \\ \rm{\large{ \rightarrow \: 3 \sqrt{147} }} \\ \\ \rm{\large{ \rightarrow \: 3 \sqrt{7 \times 7 \times 3} }} \\ \\ \rm{\large{ \rightarrow \: 3 \times 7 \sqrt{3} }} \\ \\ \rm{\large{ \rightarrow \boxed{ \: 21 \sqrt{3} }}}$

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$\huge{ \underline{ \underline{ \green{ \rm{B}}}}} \\ \\ \rm{\large{ \rightarrow \: \frac{7}{3} \sqrt{ \frac{1}{3} } }} \\ \\ \rm{\large{ \odot{\purple{ \: rationalizing \: factor \: of \: \sqrt{3} = \sqrt{3} }}}} \\ \\ \rm{\large{ \rightarrow \: \frac{7}{3} \sqrt{ \frac{1}{3} } \times \frac{ \sqrt{3} }{ \sqrt{3} } }} \\ \\ \rm{\large{ \rightarrow \: \frac{7}{3} \times \frac{ \sqrt{3} }{3} }} \\ \\ \rm{\large{ \rightarrow \: \boxed{ \frac{7 \sqrt{3} }{9} }}}$

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$\huge{ \underline{ \underline{ \green{ \rm{C}}}}} \\ \\ \rm{\large{ \rightarrow \: 7 \sqrt{ \frac{1}{3} }}} \\ \\ \rm{\large{ \odot{\purple{ \: similarly \: as \: b}}}} \\ \\ \rm{\large{ \rightarrow \: 7 \sqrt{ \frac{1}{3} } \times \frac{ \sqrt{3} }{ \sqrt{3} } }} \\ \\ \rm{\large{ \rightarrow \: \boxed{ \frac{7 \sqrt{3} }{3} }}}$

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✺Final Solution:

We had our equation,

$\rm{\large{ \rightarrow \: 3 \sqrt{147} - \frac{7}{3} \sqrt{ \frac{1}{3} } + \frac{7 \sqrt{3} }{3} }} \\ \\ \rm{\large{ \green{ \rightarrow \: A - B+ C}}}$

After simplification,

$\rm{\large{ \rightarrow \: 21 \sqrt{3} - \frac{7 \sqrt{3} }{9} + \frac{7 \sqrt{3} }{3} }} \\ \\ \rm{\large{ \odot{\purple{ \: taking \: \sqrt{3} \: as \: common}}}} \\ \\ \rm{\large{ \rightarrow \: \sqrt{3} ( 21 - \frac{7}{9} + \frac{7}{3}) }} \\ \\ \rm{\large{ \rightarrow \: \sqrt{3} ( \frac{189 - 7 + 21}{9} }}) \\ \\ \rm{\large{ \rightarrow \: \sqrt{3} ( \frac{210 - 7}{9} }}) \\ \\ \rm{\large{ \rightarrow \: \boxed{ \frac{203 \sqrt{3} }{9} }}}$

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✺Final Answer:

$\huge{ \rm{ \boxed{ = \: \: \frac{203 \sqrt{3} }{9} }}}$

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Answer 2

$\purple{\underline{\underline{\pink{\boxed{\boxed{\red{\star{\sf Question:}}}}}}}}$

$\rm{ 3 \sqrt{147} - \frac{7}{3} \sqrt{ \frac{1}{3} } + 7\sqrt{ \frac{1}{3} }}$

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$\purple{\underline{\underline{\orange{\boxed{\boxed{\green{\star{\sf Answer:}}}}}}}}$

$\rm{\green{ \boxed{\orange{ \implies \frac{203 \sqrt{3} }{9} }}}}$

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$\pink{\underline{\underline{\blue{\boxed{\boxed{\red{\star{\sf Solution:}}}}}}}}$

$\rm{Let's \ simplify \ the \ terms \ individually. }$

$\rm{Let,}$

$\boxed{ \rm{ \blue{3 \sqrt{147} }}} - \boxed{ \rm{ \blue{\frac{7}{3} \sqrt{ \frac{1}{3} } }}} \: + \: \boxed{ \rm{ \blue{7 \sqrt{ \frac{1}{3} } }}} \\ \: \: \: \: \: \: \: \: \: \downarrow \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \downarrow \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \downarrow \\ \rm{ \: \: \: \: \: \: \: \: 1 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 2 \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: 3}$

$\rm{Simplying \ Each \ term \ = \implies \ 1, \ 2, \ 3,}$

$\rm{\green{\boxed{ \underline{ \purple{1}}}}}$

$\rm{ \implies \: 3 \sqrt{147} }$

$\rm{\implies{ \: 3 \sqrt{7 \times 7 \times 3} }}$

$\rm{\implies{ \: 3 \times 7 \sqrt{3} }}$

$\rm{\implies{\pink{\boxed{ \: 21 \sqrt{3} }}}}$

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$\rm{\green{\boxed{ \underline{ \purple{2}}}}}$

$\rm{\implies{ \: \frac{7}{3} \sqrt{ \frac{1}{3} } }} \\ \\ \rm{\implies{ \: rationalizing \: factor \: of \: \sqrt{3} = \sqrt{3} }} \\ \\ \rm{\implies{ \: \frac{7}{3} \sqrt{ \frac{1}{3} } \times \frac{ \sqrt{3} }{ \sqrt{3} } }} \\ \\ \rm{\implies{ \: \frac{7}{3} \times \frac{ \sqrt{3} }{3} }} \\ \\ \rm{\implies{\pink{ \boxed{ \frac{7 \sqrt{3} }{9} }}}}$

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$\rm{\green{\boxed{ \underline{ \purple{2}}}}}$

$\rm{\implies{ \: 7 \sqrt{ \frac{1}{3} }}} \\ \\ \rm{\implies{\orange{ \: similarly \: as \: b}}} \\ \\ \rm{\implies{ \: 7 \sqrt{ \frac{1}{3} } \times \frac{ \sqrt{3} }{ \sqrt{3} } }} \\ \\ \rm{ \implies{\boxed{ \frac{7 \sqrt{3} }{3} }}}$

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$\rm{We \ had \ equation,}$

$\rm{\implies{ \: 3 \sqrt{147} - \frac{7}{3} \sqrt{ \frac{1}{3} } + \frac{7 \sqrt{3} }{3} }} \\ \\ \rm{ \green{ \implies \: 1 - 2+ 3}}$

$\rm{After \ simplification, }$

$\rm{We \ get }$

$\rm{ \implies \: 21 \sqrt{3} - \frac{7 \sqrt{3} }{9} + \frac{7 \sqrt{3} }{3} } \\ \\ \rm{\implies{ \: taking \: \sqrt{3} \: as \: common}} \\ \\ \rm{\implies{ \: \sqrt{3} ( 21 - \frac{7}{9} + \frac{7}{3}) }} \\ \\ \rm{\implies{ \: \sqrt{3} ( \frac{189 - 7 + 21}{9}) }} \\ \\ \rm{\implies{ \: \sqrt{3} ( \frac{210 - 7}{9} )} } \\ \\ \rm{\implies{ \frac{203 \sqrt{3} }{9} }}$

$\rm\green{Final \ answer:}$

$\rm{\green{ \boxed{\orange{ \implies \frac{203 \sqrt{3} }{9} }}}}$

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$\rm\red{Hope \ it \ helps \ :))}$