Question

rationalise the denominator of 1/root 5+root6-root2

Answer 1

Answer:

1/(√5 + √6  - √2) =(3√5 + √6 - 9√2  + 4√15)/39

Step-by-step explanation:

rationalise the denominator of 1/root 5+root6-root2

1/(√5 + √6  - √2)

= (1/(√5 + √6  - √2) ) *(√5 + √6  + √2)/(√5 + √6  + √2)

= (√5 + √6  + √2) / ( (√5 + √6)² - √2²)

= (√5 + √6  + √2) / ( 5 +6 + 2√30 - 2)

= (√5 + √6  + √2) / ( 9 + 2√30)

Again rationalizing

= ((√5 + √6  + √2) / ( 9 + 2√30) ) *  ( 9 - 2√30)/ ( 9 + 2√30)

= ((√5 + √6  + √2) * ( 9 - 2√30) )) / ( 9² - (2√30)²)

= (9√5 + 9√6  + 9√2  - 10√6  -12√5 - 4√15)/(81 - 120)

= ( -3√5 - √6 + 9√2- 4√15)/(-39)

= (3√5 + √6 - 9√2  + 4√15)/39

Answer 2

Answer:

Step-by-step explanation:

1/root5+root6-root2=1/root9

=>1*root9/root9*root9

=>root9/9

=>3/9=>1/3

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