How do you simplify (2sqrt7+ sqrt3)(3sqrt7 + √2)(2√7+√3)(3√7+√2)?

1 Answer
Gaya3
Oct 13, 2017

14+2sqrt14+3sqrt21+sqrt614+2√14+3√21+√6

Explanation:

(color(red)(2sqrt7)+color(green)(sqrt3))(color(blue)(3sqrt7)+color(orange)(sqrt2))(2√7+√3)(3√7+√2)

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)=2√7⋅3√7+2√7√2+3√7√3+√2√3

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

=42+2sqrt14+3sqrt21+sqrt6=42+2√14+3√21+√6

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

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