Answer:
- 31[tex]\sqrt{6}[/tex]
Step-by-step explanation:
Assuming you require the expression simplified.
Using the rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]
Simplifying the radicals
[tex]\sqrt{24}[/tex] = [tex]\sqrt{4(6)}[/tex] = [tex]\sqrt{4}[/tex] × [tex]\sqrt{6}[/tex] = 2[tex]\sqrt{6}[/tex]
[tex]\sqrt{216}[/tex] = [tex]\sqrt{36(6)}[/tex] = [tex]\sqrt{36}[/tex] × [tex]\sqrt{6}[/tex] = 6[tex]\sqrt{6}[/tex]
[tex]\sqrt{54}[/tex] = [tex]\sqrt{9(6)}[/tex] = [tex]\sqrt{9}[/tex] × [tex]\sqrt{6}[/tex] = 3[tex]\sqrt{6}[/tex]
[tex]\sqrt{600}[/tex] = [tex]\sqrt{100(6)}[/tex] = [tex]\sqrt{100}[/tex] × [tex]\sqrt{6}[/tex] = 10[tex]\sqrt{6}[/tex]
Thus
12(2[tex]\sqrt{6}[/tex] ) - 3(6[tex]\sqrt{6}[/tex] ) - 5(3[tex]\sqrt{6}[/tex] ) - 10[tex]\sqrt{6}[/tex]
= 24[tex]\sqrt{6}[/tex] - 18[tex]\sqrt{6}[/tex] - 15[tex]\sqrt{6}[/tex] - 10[tex]\sqrt{6}[/tex]
= (24 - 18 - 15 - 10)[tex]\sqrt{6}[/tex]
= - 31[tex]\sqrt{6}[/tex]
