Solve for x square root of x

$\sqrt{x} < 14$

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

${\sqrt{x}}^{2} < 14^{2}$

Simplify each side of the inequality.

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

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

$x^{\frac{1}{2} \cdot 2} < 14^{2}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$x^{\frac{1}{2} \cdot 2} < 14^{2}$

Rewrite the expression.

$x^{1} < 14^{2}$

Simplify.

$x < 14^{2}$

Raise $14$ to the power of $2$ .

$x < 196$

Find the domain of $\sqrt{x} - 14$ .

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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.

$[0, \infty)$

Use each root to create test intervals.

$0 < x < 196$

$x > 196$

Choose a test value from each interval and plug this value into the original inequality to determine which intervals satisfy the inequality.

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Test a value on the interval $0 < x < 196$ to see if it makes the inequality true.

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Choose a value on the interval $0 < x < 196$ and see if this value makes the original inequality true.

$x = 2$

Replace $x$ with $2$ in the original inequality.

$\sqrt{2} < 14$

The left side $1.41421356$ is less than the right side $14$ , which means that the given statement is always true.

True

Test a value on the interval $x > 196$ to see if it makes the inequality true.

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Choose a value on the interval $x > 196$ and see if this value makes the original inequality true.

$x = 198$

Replace $x$ with $198$ in the original inequality.

$\sqrt{198} < 14$

The left side $14.07124727$ is not less than the right side $14$ , which means that the given statement is false.

False

Compare the intervals to determine which ones satisfy the original inequality.

$0 < x < 196$ True

$x > 196$ False

$0 < x < 196$ True

$x > 196$ False

The solution consists of all of the true intervals.

$0 < x < 196$

The result can be shown in multiple forms.

Inequality Form:

$0 < x < 196$

Interval Notation:

$(0, 196)$

Solve for x square root of x<14

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