Question

Rationalise 10/√7-√2 ​

Answer 1

`(10)/(√(7) ) -√(2) =(10√(7) -7√(2) )/(7)`

( Decimal:
`2.36543...`)

Steps:

1: Convert element to fraction.

`√(2) =(√(2)√(7) )/(√(7) )`

`=(10)/(√(7) ) -(√(2) √(7) )/(√(7) )`

2: Since denominator are equal, combine the fractions.

`(a)/(c)` ±
`(b)/(c) =(a+b)/(c)`

`=(10-√(2) √(7) )/(√(7) )`

-----------------------

`√(2) √(7) =√(14)`

`=(10-√(14) )/(√(7) )`

Rationalize
`(10-√(14) )/(√(7) )` :
`(10√(7) -7√(2) )/(7)`

`=\frac{10√(7)-7√(2) }7}`

Answer 2

`(10)/( √(7) - √(2) ) \\ = (10)/( √(7) - √(2) ) * ( √(7) + √(2) )/( √(7) + √(2) ) \\ = (10( √(7) + √(2)) )/(( √(7) - √(2) )( √(7) + √(2) )) \\ = \frac{10 √(7) + 10 √(2) }{( { √(7) )}^(2) - ( √(2) ) ^(2) } \\ = (10( √(7) + √(2) ))/(7 - 2) \\ = (10( √(7) + √(2) ) )/(5) \\ = 2( √(7) + √(2) ) \\ = 2 √(7) + 2 √(2)`