what is the following product?\n$sqrt3{24}cdotsqrt3{45}$\n$sqrt3{69}$\n$4(sqrt3{6})$\n$6(sqrt3{5})$\n$6(sqrt3…
what is the following product?\n$sqrt3{24}cdotsqrt3{45}$\n$sqrt3{69}$\n$4(sqrt3{6})$\n$6(sqrt3{5})$\n$6(sqrt3{10})$
Answer
Explanation:
Step1: Rewrite the radicals
Use the property $\sqrt[3]{a}\cdot\sqrt[3]{b}=\sqrt[3]{ab}$. So, $\sqrt[3]{24}\cdot\sqrt[3]{45}=\sqrt[3]{24\times45}$.
Step2: Calculate the product inside the radical
$24\times45 = 1080$.
Step3: Prime - factorize 1080
$1080=2^{3}\times3^{3}\times5$.
Step4: Simplify the cube - root
$\sqrt[3]{1080}=\sqrt[3]{2^{3}\times3^{3}\times5}=2\times3\sqrt[3]{5}=6\sqrt[3]{5}$.
Answer:
$6(\sqrt[3]{5})$