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
[tex]\sqrt{45}[/tex]
= [tex]\sqrt{9(5)}[/tex] = [tex]\sqrt{9}[/tex] × [tex]\sqrt{5}[/tex] = 3[tex]\sqrt{5}[/tex]
[tex]\sqrt{20}[/tex]
= [tex]\sqrt{4(5)}[/tex] = [tex]\sqrt{4}[/tex] × [tex]\sqrt{5}[/tex] = 2[tex]\sqrt{5}[/tex]
Then
[tex]\sqrt{45}[/tex] - 3[tex]\sqrt{20}[/tex] + 4[tex]\sqrt{5}[/tex]
= 3[tex]\sqrt{5}[/tex] - 3(2[tex]\sqrt{5}[/tex] ) + 4[tex]\sqrt{5}[/tex]
= 3[tex]\sqrt{5}[/tex] - 6[tex]\sqrt{5}[/tex] + 4[tex]\sqrt{5}[/tex]
= [tex]\sqrt{5}[/tex]
