Question

Using the fact that \(x^{1 / 2}=\sqrt{x}\), rewrite in simplest radical form. $$18^{1 / 2} x \cdot 9 x^{1 / 2} x$$

Short answer

The simplest radical form of the given expression is \(27\sqrt{2}x^{3 / 2}\)

Step-by-step solution

Write down the given expression

The given expression is \(18^{1 / 2} x \cdot 9 x^{1 / 2} x\).

Simplify the square root

Transform \(18^{1 / 2}\) into radical form, \(\sqrt{18}\). The expression becomes \(\sqrt{18} x \cdot 9x^{1 / 2} x\).

Simplify the radical

Simplify the \(\sqrt{18}\) to \(3\sqrt{2}\), because \(18= 9*2\), and that leads to \(3\sqrt{2}\), due to the fact that the square root of \(9\) is \(3\). The expression becomes \(3\sqrt{2}x \cdot 9x^{1 / 2} x\).

Simplify the terms

Now, use the properties of radicals to multiply the like terms. The expression \(3\sqrt{2}x \cdot 9x^{1 / 2} x\) simplifies to \(27\sqrt{2}x^{3 / 2}\).