Question

Which expression is equivalent to (4 sqrt of 6)/(cube root of 2)?

a - (12 sqrt of 27)/2
b - (4 sqrt of 24)/2
c- (12 sqrt of 55296)/2
(12 sqrt of 177147)/3

Answer 1

A!!!!

12^sqrt 27/ 2

Explanation:

Answer 2

For this case we must find an expression equivalent to:

`\frac{4√(6)}{\sqrt[3]{2}}`

We multiply by:

`(\frac{(\sqrt[3]{2})^2}{(\sqrt[3]{2})^2})\\\frac{4√(6)}{\sqrt[3]{2}}*(\frac{(\sqrt[3]{2})^2}{(\sqrt[3]{2})^2})=`

By definition of multiplication of powers of the same base we have:

`a^n*a^m=a^(m+n)\\\frac{4√(6)*(\sqrt[3]{2})^2}{(\sqrt[3]{2})^3}=\\\frac{4√(6)*(\sqrt[3]{2})^2}{2}=`

Move the exponent within the radical:

`\frac{4√(6)*\sqrt[3]{2^2}}{2}=\\\frac{4√(6)*\sqrt[3]{4}}{2}=`

We rewrite:

`4^{(1)/(3)}=4^{(2)/(6)}=\sqrt[6]{4^2}\\6^{(1)/(2)}=6^{(3)/(6)}=\sqrt[6]{6^3}`

Rewriting the expression:

`\frac{4\sqrt[6]{4^2}\sqrt[6]{6^3}}{2}=\\\frac{4\sqrt[6]{16*216}}{2}=\\\frac{4\sqrt[6]{3456}}{2}=\\\frac{4\sqrt[6]{2^6*54}}{2}=\\\frac{8\sqrt[6]{54}}{2}=\\4\sqrt[6]{54}`

Answer:

`4\sqrt[6]{54}`