Chapter 9, Problem 7CA

To determine

To determine which expressions are in simplest form.

Answer to Problem 7CA

Expressions, $x\sqrt{45x}$ , $\sqrt[3]{\frac{4}{9}}$ , $16\sqrt{5}$ , $3x\sqrt{5x}$ , $\frac{4\sqrt{7}}{3}$

  $2\sqrt[3]{x^2}$ ,are in their simplest form.

Explanation of Solution

Given:

Expressions:

  $x\sqrt{45x}$

  $\frac{16}{\sqrt{5}}$

  $\sqrt[3]{\frac{4}{9}}$

  $16\sqrt{5}$

  $3x\sqrt{5x}$

  $\frac{\sqrt[3]{x^4}}{2}$

  $\frac{4\sqrt{7}}{3}$

  $\frac{\sqrt{16}}{5}$

  $2\sqrt[3]{x^2}$

  $3\frac{\sqrt{7}}{\sqrt{x}}$

Calculation:

Expression, $x\sqrt{45x}$ is in its simplest form.

Expression, $\frac{16}{\sqrt{5}}$ can further be simplified as,

Multiply and divide by $\sqrt{5}$

So,

  $\frac{16\times \sqrt{5}}{\sqrt{5}\times \sqrt{5}}$

So it can besimplified as, $\frac{16\sqrt{5}}{5}$

Expression, $\sqrt[3]{\frac{4}{9}}$ is in its simplest form.

Expression, $16\sqrt{5}$ is in its simplest form.

Expression, $3x\sqrt{5x}$ is in its simplest form.

Expression, $\frac{\sqrt[3]{x^4}}{2}$ can further be simplified as,

On solving the cube root,

So it can be simplified as, $\frac{x\sqrt[3]{x}}{2}$

Expression, $\frac{4\sqrt{7}}{3}$ is in its simplest form.

Expression, $\frac{\sqrt{16}}{5}$ can further be simplified as,

On solving the root,

So it can be simplified as, $\frac{4}{5}$

Expression, $2\sqrt[3]{x^2}$ is in its simplest form.

Expression, $3\frac{\sqrt{7}}{\sqrt{x}}$ can further be simplified as,

Multiply and divide by $\sqrt{x}$

So,

  $3\frac{\sqrt{7}\times \sqrt{x}}{\sqrt{x}\times \sqrt{x}}$

So it can be simplified as, $3\frac{\sqrt{7x}}{x}$ .