Answer:
see explanation
Step-by-step explanation:
Using the rule of radicals
[tex]\sqrt{a}[/tex] × [tex]\sqrt{b}[/tex] ⇔ [tex]\sqrt{ab}[/tex], thus
[tex]\frac{ab}{c}[/tex]
= [tex]\frac{\sqrt{2}\sqrt{10} }{\sqrt{5} }[/tex]
= [tex]\frac{\sqrt{20} }{\sqrt{5} }[/tex]
= [tex]\frac{\sqrt{4(5)} }{\sqrt{5} }[/tex]
= [tex]\frac{2\sqrt{5} }{\sqrt{5} }[/tex] ← cancel [tex]\sqrt{5}[/tex]
= 2
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(a)
Given
9[tex]\sqrt{3}[/tex] - 4[tex]\sqrt{3}[/tex] + [tex]\sqrt{5}[/tex] + 2[tex]\sqrt{5}[/tex]
Collect like radicals, that is
(9 - 4)[tex]\sqrt{3}[/tex] + (1 + 2)[tex]\sqrt{5}[/tex]
= 5[tex]\sqrt{3}[/tex] + 3[tex]\sqrt{5}[/tex]
(b)
Given
10[tex]\sqrt{2}[/tex] + 4[tex]\sqrt{7}[/tex] - 6[tex]\sqrt{2}[/tex]
Collect like radicals
= (10 - 6)[tex]\sqrt{2}[/tex] + 4[tex]\sqrt{7}[/tex]
= 4[tex]\sqrt{2}[/tex] + 4[tex]\sqrt{7}[/tex]
