Algebra Examples

$\sqrt{x} \geq 1$

Step 1

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

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

Step 2

Simplify each side of the inequality.

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

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

Simplify the left side.

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

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

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

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

Cancel the common factor of $2$ .

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Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

$x \geq 1^{2}$

Simplify the right side.

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One to any power is one.

$x \geq 1$

Step 3

Find the domain of $\sqrt{x} - 1$ .

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Set the radicand in $\sqrt{x}$ greater than or equal to $0$ to find where the expression is defined.

$x \geq 0$

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.

$x \geq 1$

Step 5