1.

Factorise `x^(2)+6sqrt(6)x+48`.

Answer» Here, `a=1, b=6sqrt(6), c=48`
`therefore a xx c=48`
`48=2xx2xx2xx2xx3`
`=sqrt(2)xxsqrt(2)xx2xx2xx2xxsqrt(3)xxsqrt(3)`
`=2sqrt(6)xx4sqrt(6)`
Now, we take two factors of 48 whose sum is `6sqrt(6)`
Such factors are `2sqrt(6)` and `4sqrt(6)`
`therefore x^(2)+6sqrt(6)x+48=x^(2)+2sqrt(6)x+4sqrt(6)x+48`
`=x(x+2sqrt(6))+4sqrt(6)(x+2sqrt(6))`
`=(x+2sqrt(6))(x+4sqrt(6))`


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