Answer:
8[tex]\sqrt{6}[/tex]
Step-by-step explanation:
Using the rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] = [tex]\sqrt{ab}[/tex]
Simplifying the given radicals
[tex]\sqrt{294}[/tex]
= [tex]\sqrt{49(6)}[/tex]
= [tex]\sqrt{49}[/tex] × [tex]\sqrt{6}[/tex] = 7[tex]\sqrt{6}[/tex]
[tex]\sqrt{24}[/tex]
= [tex]\sqrt{4(6)}[/tex]
= [tex]\sqrt{4}[/tex] × [tex]\sqrt{6}[/tex] = 2[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]
Hence
7[tex]\sqrt{6}[/tex] - 2[tex]\sqrt{6}[/tex] + 3[tex]\sqrt{6}[/tex]
= 8[tex]\sqrt{6}[/tex]
