Question

Simply the following expression. Assume that all variables are positive.

Answer 1

To simplify the expression, first, we express the number 48 in its prime factors.

48 | 2

24 | 2

12 | 2

6 | 2

3 | 3

1

$48=2\cdot2\cdot2\cdot2\cdot3=2^2\cdot2^2\cdot3$

Then, we replace it for the number inside the root

$\sqrt[]{48x^{10}y^2}=\sqrt[]{2^2\cdot2^2\cdot3x^{10}\cdot y^2}^{}$

Then, we divide each exponent of each power by the root (2), that way we will be able to simplify the root for those powers

$2\cdot2x^5y\sqrt[]{3}=4x^5y\sqrt[]{3}$

Notice that 2/2 = 1 and 10/2 = 5.

Hence, the simplest expression is

$4x^5y\sqrt[]{3}$