Answer:
Given,
[tex]\frac{4\sqrt{3} }{\sqrt{6} -\sqrt{2} }[/tex]
To Find,
Rationalize the denominator of [tex]\frac{4\sqrt{3} }{\sqrt{6} -\sqrt{2} }\\[/tex]
Solution,
We can simply solve this mathematical problem by using the following mathematical steps.
Rationalizing the denominator:
= [tex]\frac{4\sqrt{3} }{\sqrt{6} -\sqrt{2} }[/tex] × [tex]\frac{\sqrt{6} +\sqrt{2} }{\sqrt{6} +\sqrt{2} }[/tex]
We know that (a - b)(a + b) =(a² - b²)
= [tex]\frac{4\sqrt{3}(\sqrt{6} +\sqrt{2} ) }{(\sqrt{6} )^{2} -(\sqrt{2})^{2} }[/tex]
= [tex]\frac{4\sqrt{3}(\sqrt{6} +\sqrt{2} ) }{4}[/tex]
= [tex]{\sqrt{3}(\sqrt{6} +\sqrt{2} ) }[/tex]
=[tex]\sqrt{18} +\sqrt{6}[/tex]
Therefore, the final answer is [tex]3\sqrt{2} +\sqrt{6}[/tex]
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Answers & Comments
Answer:
Given,
[tex]\frac{4\sqrt{3} }{\sqrt{6} -\sqrt{2} }[/tex]
To Find,
Rationalize the denominator of [tex]\frac{4\sqrt{3} }{\sqrt{6} -\sqrt{2} }\\[/tex]
Solution,
We can simply solve this mathematical problem by using the following mathematical steps.
Rationalizing the denominator:
= [tex]\frac{4\sqrt{3} }{\sqrt{6} -\sqrt{2} }[/tex] × [tex]\frac{\sqrt{6} +\sqrt{2} }{\sqrt{6} +\sqrt{2} }[/tex]
We know that (a - b)(a + b) =(a² - b²)
= [tex]\frac{4\sqrt{3}(\sqrt{6} +\sqrt{2} ) }{(\sqrt{6} )^{2} -(\sqrt{2})^{2} }[/tex]
= [tex]\frac{4\sqrt{3}(\sqrt{6} +\sqrt{2} ) }{4}[/tex]
= [tex]{\sqrt{3}(\sqrt{6} +\sqrt{2} ) }[/tex]
=[tex]\sqrt{18} +\sqrt{6}[/tex]
Therefore, the final answer is [tex]3\sqrt{2} +\sqrt{6}[/tex]