Pre-Algebra Examples

$2 \sqrt{7 x y}$

Step 1

Divide each term in $2 \sqrt{7 x y} = 0$ by $2$ and simplify.

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Step 1.1

Divide each term in $2 \sqrt{7 x y} = 0$ by $2$ .

$\frac{2 \sqrt{7 x y}}{2} = \frac{0}{2}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $2$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{2 \sqrt{7 x y}}{2} = \frac{0}{2}$

Step 1.2.1.2

Divide $\sqrt{7 x y}$ by $1$ .

$\sqrt{7 x y} = \frac{0}{2}$

Step 1.3

Simplify the right side.

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Step 1.3.1

Divide $0$ by $2$ .

$\sqrt{7 x y} = 0$

Step 2

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

${\sqrt{7 x y}}^{2} = 0^{2}$

Step 3

Simplify each side of the equation.

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Step 3.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7 x y}$ as ${(7 x y)}^{\frac{1}{2}}$ .

${({(7 x y)}^{\frac{1}{2}})}^{2} = 0^{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify ${({(7 x y)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1

Multiply the exponents in ${({(7 x y)}^{\frac{1}{2}})}^{2}$ .

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Step 3.2.1.1.1

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

${(7 x y)}^{\frac{1}{2} \cdot 2} = 0^{2}$

Step 3.2.1.1.2

Cancel the common factor of $2$ .

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Step 3.2.1.1.2.1

Cancel the common factor.

${(7 x y)}^{\frac{1}{2} \cdot 2} = 0^{2}$

Step 3.2.1.1.2.2

Rewrite the expression.

${(7 x y)}^{1} = 0^{2}$

Step 3.2.1.2

Simplify.

$7 x y = 0^{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

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

$7 x y = 0$

Step 4

Divide each term in $7 x y = 0$ by $7 y$ and simplify.

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Step 4.1

Divide each term in $7 x y = 0$ by $7 y$ .

$\frac{7 x y}{7 y} = \frac{0}{7 y}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $7$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{7 x y}{7 y} = \frac{0}{7 y}$

Step 4.2.1.2

Rewrite the expression.

$\frac{x y}{y} = \frac{0}{7 y}$

Step 4.2.2

Cancel the common factor of $y$ .

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Step 4.2.2.1

Cancel the common factor.

$\frac{x y}{y} = \frac{0}{7 y}$

Step 4.2.2.2

Divide $x$ by $1$ .

$x = \frac{0}{7 y}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Cancel the common factor of $0$ and $7$ .

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Step 4.3.1.1

Factor $7$ out of $0$ .

$x = \frac{7 (0)}{7 y}$

Step 4.3.1.2

Cancel the common factors.

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Step 4.3.1.2.1

Factor $7$ out of $7 y$ .

$x = \frac{7 (0)}{7 (y)}$

Step 4.3.1.2.2

Cancel the common factor.

$x = \frac{7 \cdot 0}{7 y}$

Step 4.3.1.2.3

Rewrite the expression.

$x = \frac{0}{y}$

Step 4.3.2

Divide $0$ by $y$ .

$x = 0$

Step 5

To find the end points, substitute the bounds of the $y$ values from the domain into $f (y) = 0$ .

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Step 5.1

Replace the variable $y$ with $S E T, x | x E R$ in the expression.

$f (S E T, x | x E R) = 0$

Step 5.2

The final answer is $0$ .

$0$

Step 5.3

Replace the variable $y$ with $\infty$ in the expression.

$f (\infty) = 0$

Step 5.4

The final answer is $0$ .

$0$

Step 6

The end points are $(0, S E T, x | x E R), (0, \infty)$ .

$(0, S E T, x | x E R), (0, \infty)$

Step 7

The square root can be graphed using the points around the vertex $(0, S E T, x | x E R), (0, \infty),$

$\begin{array}{c} x & y \\ 0 & S E \\ 0 & \infty \end{array}$

Step 8