Math, asked by yashovardhansharma20, 4 hours ago

rationalize the denominator = 6-4√3/6+4√3​

Answers

Answered by adiwan2
1

Answer:

4 \sqrt{3}  - 7

Step-by-step explanation:

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

 =\left(\dfrac{6 - 4 \sqrt{3} }{6 + 4 \sqrt{3} }\right) \left(\dfrac{6 - 4 \sqrt{3} }{6  -  4 \sqrt{3} }  \right)

 =\dfrac{(6 - 4 \sqrt{3})^{2}  }{6^{2}   - (4 \sqrt{3})^{2}  }

=  \dfrac{ {6}^{2} +   {(4 \sqrt{3} )}^{2}   - 2(6)(4 \sqrt{3} ) }{36  -  48}

  = \dfrac{36 + 48  - 48 \sqrt{3} }{36 - 48}

 =  \dfrac{84 - 48 \sqrt{3} }{ - 12}  = 4 \sqrt{3}  - 7

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