Question

Please help me on these 2. Quickly :(

NUMBER ONE..... 4x^5/6 in radical form?

NUMBER TWO..... Rationalize the denominator of 7/(3+ SQRT 3)

Answer 1

First. you've got to know this:\[a ^{\frac{ b }{ c }}=(\sqrt[c]{a})^b =\sqrt[c]{a^b}\]Then apply to 4x^(5/6):\[4x ^{\frac{ 5 }{ 6 }}=4\sqrt[6]{x^5}\]

Answer 2

For the second one, you need to know a trick: multiply both nominator and denominator with 3 - sqrt 3:\[\frac{ 7 }{ 3+\sqrt{3} }\frac{ 3-\sqrt 3 }{ 3-\sqrt 3 }\]
You'll remember that\[(a+b)(a-b)=a^2-b^2 \]
Applying this gives:\[\frac{ 7(3-\sqrt 3) }{ 9 - 3 }=\frac{ 21-7\sqrt 3 }{ 6 }\]
Once you've seen this trick, you will always remember it as a way to rationalize the denominator!