Question

Find the answer please!!​

Answer 1

Solution

We have to simplify the given expression

• $\sf{2 \sqrt{3} + \dfrac{4}{\sqrt{3}} - 5 \sqrt{3}}$

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Firstly, we will summarize the given expression and then see what is common between them.

$\tt\dashrightarrow{\dfrac{4}{\sqrt{3}} + 2 \sqrt{3} - 5 \sqrt{3}}$

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$\tt\dashrightarrow{\dfrac{4}{\sqrt{3}} - 3 \sqrt{3}}$

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Now, we can write this expression as

$\: \: \: \: \: \: \: \: \bullet\bf\: \: \: {\dfrac{4}{\sqrt{3}} - \dfrac{3 \sqrt{3}}{1}}$

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Now we can take the LCM and solve the problem by simplifying it.

$\tt\dashrightarrow{\dfrac{4 - \sqrt{3} ( 3 \sqrt{3})}{\sqrt{3}}}$

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$\tt\dashrightarrow{\dfrac{4 - 9}{\sqrt{3}}}$

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$\tt\dashrightarrow{\dfrac{-5}{\sqrt{3}}}$

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Rationalising the denominator

$\tt\dashrightarrow{\dfrac{-5}{\sqrt{3}} \times \dfrac{\sqrt{3}}{\sqrt{3}}}$

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$\tt\dashrightarrow{\dfrac{-5 \times \sqrt{3}}{\sqrt{3} \times \sqrt{3}}}$

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$\bf\dashrightarrow{\dfrac{-5 \sqrt{3}}{3}}$

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Hence,

• The simplified value of the given expression is $\sf{\dfrac{-5 \sqrt{3}}{3}}$.

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