How do you simplify $(3 \sqrt{3} - 4 \sqrt{2}) (2 \sqrt{3} + 4 \sqrt{2})$ $(3sqrt3 - 4sqrt2)(2sqrt3 + 4sqrt2)$ ?

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Answer 1 · 2016-09-10T13:11:51

$= 4 \sqrt{6} - 14$ $=4sqrt6 -14$

Recall: $\sqrt{x} \times \sqrt{x} = \sqrt{x^{2}} = {(\sqrt{x})}^{2} = x$ $sqrtx xx sqrtx = sqrt(x^2) = (sqrtx)^2 = x$

and $\sqrt{x} \times \sqrt{y} = \sqrt{x y}$ $sqrt x xx sqrty = sqrt(xy)$

Each term in the first bracket must be multiplied by each term in the second bracket. This will give 4 terms, which might simplify.

$(3 \sqrt{3} - 4 \sqrt{2}) (2 \sqrt{3} + 4 \sqrt{2})$ $(3sqrt3 - 4sqrt2)(2sqrt3 + 4sqrt2)$

= $6 \times 3 + 12 \sqrt{6} - 8 \sqrt{6} - 16 \times 2$ $6xx3 +12sqrt6-8sqrt6 -16xx2$

= $18 + 4 \sqrt{6} - 32$ $18+4sqrt6-32$

$= 4 \sqrt{6} - 14$ $=4sqrt6 -14$

How do you simplify (3√3−4√2)(2√3+4√2)(3sqrt3 - 4sqrt2)(2sqrt3 + 4sqrt2)?