Find the Domain square root of 64x^2

$\sqrt{64 x^{2}}$

Step 1

Set the radicand in $\sqrt{64 x^{2}}$ greater than or equal to $0$ to find where the expression is defined.

$64 x^{2} \geq 0$

Step 2

Solve for $x$ .

Divide each term in $64 x^{2} \geq 0$ by $64$ and simplify.

Divide each term in $64 x^{2} \geq 0$ by $64$ .

$\frac{64 x^{2}}{64} \geq \frac{0}{64}$

Simplify the left side.

Cancel the common factor of $64$ .

Cancel the common factor.

$\frac{64 x^{2}}{64} \geq \frac{0}{64}$

Divide $x^{2}$ by $1$ .

$x^{2} \geq \frac{0}{64}$

Simplify the right side.

Divide $0$ by $64$ .

$x^{2} \geq 0$

Since the left side has an even power, it is always positive for all real numbers.

All real numbers

Step 3

The domain of the expression is all real numbers except where the expression is undefined. In this case, there is no real number that makes the expression undefined.

Interval Notation:

$(- \infty, \infty)$

Set-Builder Notation:

${x | x \in ℝ}$

Step 4

Find the Domain square root of 64x^2

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