Question

Can someone please help with this math question:)

Answer 1

`(5+√(2) )/(23)`

Explanation:

To rationalise the denominator, multiply the numerator and denominator by the conjugate of the denominator.

the conjugate of 5 -
`√(2)` is 5 +
`√(2)` , then

=
`(1(5+√(2)) )/((5-√(2))(5+√(2)) )` ← expand denominator using aFOIL

=
`(5+√(2) )/(25-2)`

=
`(5+√(2) )/(23)`

Answer 2

The rationalisation factor for
`(1)/( a - √(b) )` is
`a + √(b)`

So, let us apply it here.

`(1)/(5 - √(2) )`

The rationalising factor for 5 - √2 is 5 + √2.

Therefore, multiplying and dividing by 5 + √2, we have

`= (1)/(5 - √(2) ) * (5 + √(2) )/(5 + √(2) ) \\ = (5 + √(2) )/((5 - √(2))(5 + √(2) ) ) \\ = \frac{5 + √(2) }{ {(5)}^(2) - ( √(2))^(2) } \\ = (5 + √(2) )/(25 - 2) \\ = (5 + √(2) )/(23)`

Answer:

`(5 + √(2) )/(23)`

Hope you could understand.

If you have any query, feel free to ask.