Math, asked by yuva111, 11 months ago

rationalise the denominators 1 by3+root 2

Answers

Answered by gaurav2013c
4

 \frac{1}{3 +  \sqrt{2} }  \\  \\  =  \frac{1}{3 +  \sqrt{2} }  \times  \frac{3 -  \sqrt{2} }{3 -  \sqrt{2} }  \\  \\  =  \frac{3 -  \sqrt{2} }{9 - 2}  \\  \\  =  \frac{3 -  \sqrt{2} }{7}

yuva111: How will came 9-2 here
gaurav2013c: by using identity ( a-b) (a+b) = a^2 - b^2
gaurav2013c: (3)^2 - (root2)^2
gaurav2013c: 9 - 2
gaurav2013c: = 7
Answered by Anonymous
2
hiii!!!

here's Ur answer...

given \:  =  >  \:  \frac{1}{3 +  \sqrt{2} }  \\  \\  =  \frac{1}{3 +  \sqrt{2} }  \times  \frac{3 -  \sqrt{2} }{3 -  \sqrt{2} }  \\  \\  =  \frac{3 -  \sqrt{2} }{(3 +  \sqrt{2} )(3 -  \sqrt{2} )}  \\  \\  =  \frac{3 -  \sqrt{2} }{( {3})^{2}  - ( { \sqrt{2} )}^{2} }  \\  \\  =  \frac{3 -  \sqrt{2} }{9 - 2}  \\  \\  =  \frac{3 -  \sqrt{2} }{7}

hope this helps..!!
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