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$(4 \sqrt{3} x y^{3}) (- 2 \sqrt{6} x^{3} y^{2}) ?$ $(4 sqrt 3xy^3) (-2 sqrt 6x^3y^2)?$ Multiply the radical expression

1 Answer

Oct 31, 2017

$- 24 \sqrt{2} x^{4} y^{5}$ $-24sqrt(2)x^4y^5$

Explanation:

$(4 \sqrt{3} x y^{3}) (- 2 \sqrt{6} x^{3} y^{2})$ $(4sqrt(3)xy^3)(-2sqrt(6)x^3y^2)$

decomposing each factor:
$XXX = (4 \times \sqrt{3} \times x \times y^{3}) \times ((- 2) \times \sqrt{6} \times x^{3} \times y^{2})$ $color(white)("XXX")=(4xxsqrt(3)xx x xx y^3)xx((-2) xx sqrt(6) xx x^3 xx y^2)$

regrouping like factors:
$XXX = (4 \times (- 2)) \times (\sqrt{3} \times \sqrt{6}) \times (x \times x^{3}) \times (y^{3} \times y^{2})$ $color(white)("XXX")=(4 xx(-2))xx(sqrt(3)xxsqrt(6))xx(x xx x^3)xx(y^3 xxy^2)$

combining like factors:
$XXX = (- 8) \times (\sqrt{18}) \times (x^{4}) \times (y^{5})$ $color(white)("XXX")=(-8) xx (sqrt(18)) xx (x^4) xx (y^5)$

simplifying the $\sqrt{18}$ $sqrt(18)$ factor
$XXX = (- 8) \times (3 \sqrt{2}) \times (x^{4}) \times (y^{5})$ $color(white)("XXX")=(-8) xx (3sqrt(2)) xx (x^4) xx (y^5)$

combining the two constant factors
$XXX = (- 24 \sqrt{2}) \times (x^{4}) \times (y^{5})$ $color(white)("XXX")=(-24sqrt(2)) xx (x^4) xx (y^5)$

back into (compressed) standard form:
$XXX = - 24 \sqrt{2} x^{4} y^{5}$ $color(white)("XXX")=-24sqrt(2)x^4y^5$

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