Math, asked by nishachauhan1576, 8 months ago

simplify 3√2 / √6 - √3 + 2√3 / √6 + 2 - 4√3 / √6-√2​

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Answers

Answered by tahseen619
68

0

Step-by-step explanation:

To Simplify:

 \dfrac{3 \sqrt{2} }{ \sqrt{6} -  \sqrt{3}}  +  \dfrac{2 \sqrt{3} }{ \sqrt{6} + 2}  -  \dfrac{4 \sqrt{3} }{ \sqrt{6} -  \sqrt{2}  }

How to Simplify:

1. All fraction contain different denominator, We have to Rationalize all.

2. Algebra Formula will use.

[a² - b² = (a + b)(a - b)]

3. After Rationalize get back to question and just add and subtract.

4. Get Answer

Solution:

Rationalizing of all terms see in attachment.

Now, Get back to the question,

(2 \sqrt{3}   +  \sqrt{6} ) + (3 \sqrt{2}  - 2 \sqrt{3} ) - (3 \sqrt{2}  +  \sqrt{6} ) \\  \\  = 2 \sqrt{3}   +   \sqrt{6}  + 3 \sqrt{2}  - 2 \sqrt{3}  - 3 \sqrt{2}  -  \sqrt{6}  \\  \\ = \cancel{2 \sqrt{3} }  +   \cancel{\sqrt{6} } + \cancel{3 \sqrt{2} } - \cancel{2 \sqrt{3} } - \cancel{3 \sqrt{2} } -  \cancel{\sqrt{6}} \\  \\  = 0

Therefore, The required answer is 0.

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Answered by VaibhavSR
4

Answer: 3\sqrt{2}+\sqrt{6}

Step-by-step explanation:

Given: \frac{3\sqrt{2} }{\sqrt{6}-\sqrt{3}  } + \frac{2\sqrt{3} }{\sqrt{6}+\sqrt{2}  } - \frac{4\sqrt{3} }{\sqrt{6}-\sqrt{2}  }

To find: Simplify the given expression.

Solution:

   \frac{3\sqrt{2} }{\sqrt{6}-\sqrt{3}  } + \frac{2\sqrt{3} }{\sqrt{6}+\sqrt{2}  } - \frac{4\sqrt{3} }{\sqrt{6}-\sqrt{2}  }

\frac{3\sqrt{2} }{\sqrt{6}-\sqrt{3}  } + \frac{2\sqrt{3}(\sqrt{6}-\sqrt{2} )-4\sqrt{3}(\sqrt{6}+\sqrt{2} )  }{(\sqrt{6})^{2} -(\sqrt{2})^{2}   }

\frac{3\sqrt{2} }{\sqrt{6}-\sqrt{3}  }+ \frac{6\sqrt{2}-2\sqrt{6}-12\sqrt{2}-4\sqrt{6}    }{6-2}

\frac{3\sqrt{2} }{\sqrt{6}-\sqrt{3}  }+( \frac{-6\sqrt{2}-6\sqrt{6}    }{6-2})

\frac{3\sqrt{2} }{\sqrt{6}-\sqrt{3}  }-( \frac{6\sqrt{2}+6\sqrt{6}    }{4})

\frac{12\sqrt{2}- [\sqrt{6}(6\sqrt{2}+6\sqrt{6}  ) -\sqrt{3} ((6\sqrt{2}+6\sqrt{6}  )) }{4(\sqrt{6}-\sqrt{3}  )}

\frac{12\sqrt{2}- [(6\sqrt{12}+36 ) - (6\sqrt{6}+6\sqrt{18}  )}{4(\sqrt{6}-\sqrt{3}  )}

\frac{12\sqrt{2}- 6\sqrt{12}-36 + 6\sqrt{6}+6\sqrt{18}  }{4(\sqrt{6}-\sqrt{3}  )}

After solving the above equation we get, 3\sqrt{2}+\sqrt{6}.

  • Hence, the required answer is  3\sqrt{2}+\sqrt{6}.

#SPJ2

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