Question

Please help on this square root problem

Answer 1

Rationalizing the denominator of the expression, it is found that the simplified expression is given by:

$\frac{\sqrt{6}(12x + 20x^2) + 3\sqrt{x} + 5\sqrt{x^3}}{x(96x - x)}$

What is the expression that we have to simplify?

It is given by:

$\frac{3 + 5\sqrt{x^2}}{4\sqrt{6x^2} - \sqrt{x}}$

We rationalize the denominator, using the subtraction of perfect squares, hence:

$\frac{3 + 5\sqrt{x^2}}{4\sqrt{6x^2} - \sqrt{x}} \times \frac{4\sqrt{6x^2} + \sqrt{x}}{4\sqrt{6x^2} + \sqrt{x}}$

Then, solving the expression:

$\frac{(3 + 5\sqrt{x^2})(4\sqrt{6x^2} + \sqrt{x})}{16(6x^2) - x}$

$\frac{12\sqrt{6x^2} + 3\sqrt{x} + 20x^2\sqrt{6} + 5\sqrt{x^3}}{96x^2 - x}$

$\frac{\sqrt{6}(12x + 20x^2) + 3\sqrt{x} + 5\sqrt{x^3}}{x(96x - x)}$

More can be learned about rationalizing at https://brainly.com/question/17110969

#SPJ1