Math, asked by sunilkalra253a, 10 months ago

rationalize the following :
 \frac{1}{8 + 5 \sqrt{2} }
plzz answer step by step... ​

Answers

Answered by ITzBrainlyGuy
1

Answer:

 =  \dfrac{1}{8 + 5 \sqrt{2} }

Multiply & divide with its conjugate

We know that

8 + 5√2 conjugate is 8 - 5√2

 =  \dfrac{1}{8 + 5 \sqrt{2} }  \times  \dfrac{8 - 5 \sqrt{2} }{8 - 5 \sqrt{2} }

Using

(a + b)(a - b) = a² - b²

 =  \dfrac{8 - 5 \sqrt{2} }{ {8}^{2} - ( {5 \sqrt{2} )}^{2}  }

 =  \dfrac{8 - 5 \sqrt{2} }{64 - 10}  \\ \\   =  \dfrac{8 - 5 \sqrt{2} }{54}

Hence Rationalised

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