Question

Simplify the expression:14\sqrt[]{6}-6\sqrt[]{24}simplifies to a\sqrt[]{b} where:our coefficient a = Answerour radicand b = Answer

Answer 1

You have the following expression:

`14\sqrt[]{6}-6\sqrt[]{24}`

In order to simplify the previous expression, conisder that 24 can be written as:

24 = 6*4 = 6*2^2

Then, you have:

`\begin{gathered} 14\sqrt[]{6}-6\sqrt[]{24}= \\ 14\sqrt[]{6}-6\sqrt[]{6\cdot2^2}= \\ 14\sqrt[]{6}-6\cdot2\sqrt[]{6}= \\ 14\sqrt[]{6}-12\sqrt[]{6}= \\ 2\sqrt[]{6} \end{gathered}`

Where in the last steo you simplify the terms becasue they are like terms due to the factor √6.

Then, you have for the required coefficients:

a = 2

b = 6