Step 1: Convert the radicals to to fractional exponent:
[tex] \sqrt{3} = 3 ^{ \frac{1}{2} } [/tex]
[tex] \sqrt[3]{18} [/tex] = [tex] 18^{ \frac{1}{3} } [/tex]
Step 2: Convert the fractional exponents to similar fractions:
LCD of 1/2 and 1/3 is 6
1/2 = 3/6 ⇒ [tex]3 \frac{1}{2} [/tex] = [tex]3 ^{ \frac{3}{6} } [/tex]
1/3 = 2/6 ⇒ [tex]18 ^{ \frac{1}{3} } [/tex] = [tex]18 ^{ \frac{2}{6} } [/tex]
Step 3: Convert to radicals:
[tex] 3^{ \frac{3}{6} } = \sqrt[6]{3 ^{3} } [/tex]
[tex]18 ^{ \frac{2}{6} } = \sqrt[6]{18 ^{2} } [/tex]
Step 4: Multiply:
[tex]( \sqrt[6]{3 ^{3} } )( \sqrt[6]{18 ^{2} }) [/tex]
[tex]( \sqrt[6]{ 3^{3} })( \sqrt[6]{18 ^{2} } )= ( \sqrt[6]{ 3^{3} } )( \sqrt[6]{(3 ^{3})(12) } [/tex]
= [tex] \sqrt[6]{(3 ^{6})(12) } [/tex]
ANSWER = [tex] 3\sqrt[6]{12} [/tex]
