Algebra Examples

$\sqrt{x} \geq 0$

Step 1

To remove the radical on the left side of the inequality, square both sides of the inequality.

${\sqrt{x}}^{2} \geq 0^{2}$

Step 2

Simplify each side of the inequality.

Tap for more steps...

Step 2.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{x}$ as $x^{\frac{1}{2}}$ .

${(x^{\frac{1}{2}})}^{2} \geq 0^{2}$

Step 2.2

Simplify the left side.

Tap for more steps...

Step 2.2.1

Simplify ${(x^{\frac{1}{2}})}^{2}$ .

Tap for more steps...

Step 2.2.1.1

Multiply the exponents in ${(x^{\frac{1}{2}})}^{2}$ .

Tap for more steps...

Step 2.2.1.1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$x^{\frac{1}{2} \cdot 2} \geq 0^{2}$

Step 2.2.1.1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 2.2.1.1.2.1

Cancel the common factor.

$x^{\frac{1}{2} \cdot 2} \geq 0^{2}$

Step 2.2.1.1.2.2

Rewrite the expression.

$x^{1} \geq 0^{2}$

Step 2.2.1.2

Simplify.

$x \geq 0^{2}$

Step 2.3

Simplify the right side.

Tap for more steps...

Step 2.3.1

Raising $0$ to any positive power yields $0$ .

$x \geq 0$

Step 3

The domain is all values of $x$ that make the expression defined.

$[0, \infty)$

Step 4

The solution consists of all of the true intervals.

$x \geq 0$

Step 5