Multiply. 3√⋅22√⋅58√⋅18−−√Enter your answer in simplest radical form.Please HELP!
Accepted Solution
A:
[tex]\boxed{3\sqrt{22}\sqrt{58}\sqrt{18}=18\sqrt{638}}[/tex]Explanation:Here we have the following expression:[tex]3\sqrt{22}\sqrt{58}\sqrt{18}[/tex]So we need to simplify that radical expression. By property of radicals we know that:[tex]\sqrt[n]{a}\sqrt[n]{b}=\sqrt[n]{ab}[/tex]So:[tex]3\sqrt{22}\sqrt{58}\sqrt{18}=3\sqrt{22\times 58 \times 18}=3\sqrt{22968}[/tex]The prime factorization of 22968 is:[tex]22968=2^3\cdot 3^2\cdot11\cdot 29[/tex]Hence:[tex]3\sqrt{22968}=3\sqrt{2^3\cdot 3^2\cdot11\cdot 29}=3\sqrt{2^2\cdot 3^2\cdot 2\cdot 11\cdot 29}[/tex]By property:[tex]\sqrt[n]{a^n}=a[/tex]So:[tex]3\sqrt{2^2\cdot 3^2\cdot 2\cdot 11\cdot 29} \\ \\ 3(2)(3)\sqrt{2\cdot 11\cdot 29}=18\sqrt{638}[/tex]Finally:[tex]\boxed{3\sqrt{22}\sqrt{58}\sqrt{18}=18\sqrt{638}}[/tex]Learn more:Radical expressions: