Question

How do you simplify `(2sqrt7+ sqrt3)(3sqrt7 + √2)`?

Answer 1

`14+2sqrt14+3sqrt21+sqrt6`

Explanation:

`(color(red)(2sqrt7)+color(green)(sqrt3))(color(blue)(3sqrt7)+color(orange)(sqrt2))`

Multiply every term in the first brackets to every term in the second bracket.

`=color(red)(2sqrt7)*color(blue)(3sqrt7)+color(red)(2sqrt7)color(orange)(sqrt2)+color(blue)(3sqrt7)color(green)(sqrt3)+color(orange)(sqrt2)color(green)(sqrt3)`

`=6times7+2sqrt(7times2)+3sqrt(7times3)+sqrt(2times3)`

`=42+2sqrt14+3sqrt21+sqrt6`

As there are no like terms, this is the final answer `uarr`.