Answer:
[tex]\sqrt{5}[/tex]
Step-by-step explanation:
Using the rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex]
Simplifying the radicals
[tex]\sqrt{20}[/tex] = [tex]\sqrt{4(5)}[/tex] = [tex]\sqrt{4}[/tex] × [tex]\sqrt{5}[/tex] = 2[tex]\sqrt{5}[/tex]
[tex]\sqrt{45}[/tex] = [tex]\sqrt{9(5)}[/tex] = [tex]\sqrt{9}[/tex] × [tex]\sqrt{5}[/tex] = 3[tex]\sqrt{5}[/tex]
Thus
- 6(2[tex]\sqrt{5}[/tex]) + 2(3[tex]\sqrt{5}[/tex]) + 7[tex]\sqrt{5}[/tex]
= - 12[tex]\sqrt{5}[/tex] + 6[tex]\sqrt{5}[/tex] + 7[tex]\sqrt{5}[/tex]
= [tex]\sqrt{5}[/tex]
