Answer:
see explanation
Step-by-step explanation:
Using the rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]
Given
(2 - 5[tex]\sqrt{8}[/tex] )(4 - 6[tex]\sqrt{3}[/tex] )
Each term in the second factor is multiplied by each term in the first factor, that is
2(4 - 6[tex]\sqrt{3}[/tex] ) - 5[tex]\sqrt{8}[/tex](4 - 6[tex]\sqrt{3}[/tex] ) ← distribute both parenthesis
= 8 - 12[tex]\sqrt{3}[/tex] - 20[tex]\sqrt{8}[/tex] + 30[tex]\sqrt{24}[/tex] → *
Simplify [tex]\sqrt{8}[/tex] and [tex]\sqrt{24}[/tex]
[tex]\sqrt{8}[/tex] = [tex]\sqrt{4(2)}[/tex] = [tex]\sqrt{4}[/tex] × [tex]\sqrt{2}[/tex] = 2[tex]\sqrt{2}[/tex]
[tex]\sqrt{24}[/tex] = [tex]\sqrt{4(6)}[/tex] = [tex]\sqrt{4}[/tex] × [tex]\sqrt{6}[/tex] = 2[tex]\sqrt{6}[/tex]
Back to *
= 8 - 12[tex]\sqrt{3}[/tex] - 20(2[tex]\sqrt{2}[/tex] ) + 30(2[tex]\sqrt{6}[/tex] )
= 8 - 12[tex]\sqrt{3}[/tex] - 40[tex]\sqrt{2}[/tex] + 60[tex]\sqrt{6}[/tex]
