Answer:
36[tex]\sqrt{10}[/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 in the expression
[tex]\sqrt{40}[/tex]
= [tex]\sqrt{4(10)}[/tex]
= [tex]\sqrt{4}[/tex] × [tex]\sqrt{10}[/tex] = 2[tex]\sqrt{10}[/tex]
[tex]\sqrt{160}[/tex]
= [tex]\sqrt{16(10)}[/tex]
= [tex]\sqrt{16}[/tex] × [tex]\sqrt{10}[/tex] = 4[tex]\sqrt{10}[/tex]
Thus
4[tex]\sqrt{40}[/tex] + 7[tex]\sqrt{160}[/tex]
= 4 × 2[tex]\sqrt{10}[/tex] + 7 × 4[tex]\sqrt{10}[/tex]
= 8[tex]\sqrt{10}[/tex] + 28[tex]\sqrt{10}[/tex]
= 36[tex]\sqrt{10}[/tex]
Answer:
Step-by-step explanation:
4[tex]4\sqrt{40} + 7 \sqrt{160} = 4\sqrt{2*2*2*5} + 7\sqrt{4*4*5*2}\\ = 4*2\sqrt{10} + 7*4\sqrt{10}\\ = 8\sqrt{10} + 28\sqrt{10} \\[/tex]
= (8 + 28)√10
= 36√10
