1.

6-4√2/6+4√2 , Simplify the given number by rationalising the denominator.

Answer»
= \frac{6 - 4 \sqrt{2} }{ 6 + 4 \sqrt{2} } \times \frac{6 - 4 \sqrt{2} }{ 6 - 4 \sqrt{2} } \\ = \frac{(6)^{2} + ( 4 \sqrt{2} ) ^{2} - 2(6)( 4 \sqrt{2}) }{(6) ^{2} - ( 4 \sqrt{2}) ^{2} } \\ = \frac{36 + 32 - 48 \sqrt{2} }{36 - 32} \\ = \frac{68 - 48 \sqrt{2} }{4} \\ = \frac{4(17 - 12 \sqrt{2}) }{4} \\ = 17 - 12 \sqrt{2}


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