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
[tex]\frac{12}{\sqrt{8} }[/tex]
To rationalise the denominator multiply the numerator/ denominator by [tex]\sqrt{8}[/tex], thus
[tex]\frac{12}{\sqrt{8} }[/tex] × [tex]\frac{\sqrt{8} }{\sqrt{8} }[/tex]
= [tex]\frac{12\sqrt{8} }{8}[/tex]
[tex]\sqrt{8}[/tex] = [tex]\sqrt{4(2)}[/tex] = 2[tex]\sqrt{2}[/tex], thus
= [tex]\frac{12(2)\sqrt{2} }{8}[/tex]
= [tex]\frac{24\sqrt{2} }{8}[/tex]
= 3[tex]\sqrt{2}[/tex] ← as required
