The result of product [tex]\sqrt[3]{24} \times \sqrt[3]{45}[/tex] is [tex]6\sqrt[3]{5}[/tex].
The product is represented as:
[tex]\sqrt[3]{24} \times \sqrt[3]{45}[/tex]
Multiply the roots
[tex]\sqrt[3]{24} \times \sqrt[3]{45}= \sqrt[3]{24\times 45}[/tex]
Rewrite the above expression as:
[tex]\sqrt[3]{24} \times \sqrt[3]{45}= (24\times 45)^{1/3}[/tex]
Expand 24
[tex]\sqrt[3]{24} \times \sqrt[3]{45}= (3 \times 8 \times 45)^{1/3}[/tex]
Express 8 as 2^3
[tex]\sqrt[3]{24} \times \sqrt[3]{45}= (3 \times 2^3 \times 45)^{1/3}[/tex]
So, we have:
[tex]\sqrt[3]{24} \times \sqrt[3]{45}= 2(3 \times 45)^{1/3}[/tex]
Express 45 as 9 * 5
[tex]\sqrt[3]{24} \times \sqrt[3]{45}= 2(3 \times 9 \times 5)^{1/3}[/tex]
Express 9 as 3^2
[tex]\sqrt[3]{24} \times \sqrt[3]{45}= 2(3 \times 3^2 \times 5)^{1/3}[/tex]
[tex]\sqrt[3]{24} \times \sqrt[3]{45}= 2(3^3 \times 5)^{1/3}[/tex]
So, we have:
[tex]\sqrt[3]{24} \times \sqrt[3]{45}= 2\times 3(5)^{1/3}[/tex]
[tex]\sqrt[3]{24} \times \sqrt[3]{45}= 6(5)^{1/3}[/tex]
Rewrite as:
[tex]\sqrt[3]{24} \times \sqrt[3]{45}= 6\sqrt[3]{5}[/tex]
Hence, the result of product [tex]\sqrt[3]{24} \times \sqrt[3]{45}[/tex] is [tex]6\sqrt[3]{5}[/tex]
Read more about products at:
https://brainly.com/question/10873737
