[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: https://brainly.com/question/13452541
#LearnWithBrainly
