Question

multiply 4√6 by 2√8​

Answer 1

Answer:

$4\sqrt{6}\times \:2\sqrt{8}=32\sqrt{3}\quad \left(\mathrm{Decimal:\quad }\:55.42563\dots \right)$

Step-by-step explanation:

$4\sqrt{6}\times \:2\sqrt{8}$

$\gray{\mathrm{Factor\:integer\:}4=2^2}$

$=2^2\sqrt{6}\times \:2\sqrt{8}$

$\gray{\mathrm{Factor\:integer\:}6=2\times \:3}$

$=2^2\sqrt{2\times \:3}\times \:2\sqrt{8}$

$\gray{\mathrm{Apply\:radical\:rule}:\quad \sqrt[n]{ab}=\sqrt[n]{a}\sqrt[n]{b}}$

$\gray{\sqrt{2\times \:3}=\sqrt{2}\sqrt{3}}$

$=2^2\sqrt{2}\sqrt{3}\times \:2\sqrt{8}$

$\gray{\mathrm{Factor\:integer\:}8=2^3}$

$=2^2\sqrt{2}\sqrt{3}\times \:2\sqrt{2^3}$

$\gray{\mathrm{Apply\:exponent\:rule}:\quad \left(a^b\right)^c=a^{bc}}$

$\gray{\sqrt{2^3}=2^{3\times \dfrac{1}{2}}}$

$=2^2\sqrt{2}\sqrt{3}\times \:2\times \:2^{3\times \dfrac{1}{2}}$

$\gray{\mathrm{Refine}}$

$=2^2\sqrt{2}\sqrt{3}\times \:2\times \:2^{\dfrac{3}{2}}$

$\gray{\mathrm{Apply\:exponent\:rule}:\quad \:a^b\times \:a^c=a^{b+c}}$

$\gray{2^2\sqrt{2}\times \:2\times \:2^{\dfrac{3}{2}}=\:2^2\times \:2\times \:2^{\dfrac{1}{2}}\times \:2^{\dfrac{3}{2}}=\:2^{2+\dfrac{1}{2}+1+\dfrac{3}{2}}}$

$=\sqrt{3}\times \:2^{2+\dfrac{1}{2}+1+\dfrac{3}{2}}$

[text]\gray{2^{2+\dfrac{1}{2}+1+\dfrac{3}{2}}=2^5}[/tex]

$=2^5\sqrt{3}$

$\gray{2^5=32}$

$=32\sqrt{3}$