Algebra Examples

$\sqrt{2 x^{2}} \div \sqrt{5 x}$

Step 1

Write $\sqrt{2 x^{2}} \div \sqrt{5 x}$ as an equation.

$y = \sqrt{2 x^{2}} \div \sqrt{5 x}$

Step 2

Find the x-intercepts.

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Step 2.1

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = \sqrt{2 x^{2}} \div \sqrt{5 x}$

Step 2.2

Solve the equation.

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Step 2.2.1

Set the numerator equal to zero.

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

Step 2.2.2

Solve the equation for $x$ .

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Step 2.2.2.1

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

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

Step 2.2.2.2

Simplify each side of the equation.

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Step 2.2.2.2.1

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

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

Step 2.2.2.2.2

Simplify the left side.

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Step 2.2.2.2.2.1

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

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Step 2.2.2.2.2.1.1

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

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Step 2.2.2.2.2.1.1.1

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

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

Step 2.2.2.2.2.1.1.2

Cancel the common factor of $2$ .

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Step 2.2.2.2.2.1.1.2.1

Cancel the common factor.

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

Step 2.2.2.2.2.1.1.2.2

Rewrite the expression.

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

Step 2.2.2.2.2.1.2

Simplify.

$2 x^{2} = 0^{2}$

Step 2.2.2.2.3

Simplify the right side.

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Step 2.2.2.2.3.1

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

$2 x^{2} = 0$

Step 2.2.2.3

Solve for $x$ .

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Step 2.2.2.3.1

Divide each term in $2 x^{2} = 0$ by $2$ and simplify.

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Step 2.2.2.3.1.1

Divide each term in $2 x^{2} = 0$ by $2$ .

$\frac{2 x^{2}}{2} = \frac{0}{2}$

Step 2.2.2.3.1.2

Simplify the left side.

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Step 2.2.2.3.1.2.1

Cancel the common factor of $2$ .

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Step 2.2.2.3.1.2.1.1

Cancel the common factor.

$\frac{2 x^{2}}{2} = \frac{0}{2}$

Step 2.2.2.3.1.2.1.2

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

$x^{2} = \frac{0}{2}$

Step 2.2.2.3.1.3

Simplify the right side.

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Step 2.2.2.3.1.3.1

Divide $0$ by $2$ .

$x^{2} = 0$

Step 2.2.2.3.2

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$x = \pm \sqrt{0}$

Step 2.2.2.3.3

Simplify $\pm \sqrt{0}$ .

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Step 2.2.2.3.3.1

Rewrite $0$ as $0^{2}$ .

$x = \pm \sqrt{0^{2}}$

Step 2.2.2.3.3.2

Pull terms out from under the radical, assuming positive real numbers.

$x = \pm 0$

Step 2.2.2.3.3.3

Plus or minus $0$ is $0$ .

$x = 0$

Step 2.2.3

Exclude the solutions that do not make $0 = \sqrt{2 x^{2}} \div \sqrt{5 x}$ true.

$No solution$

Step 2.3

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

x-intercept(s): $None$

Step 3

Find the y-intercepts.

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Step 3.1

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = \sqrt{2 {(0)}^{2}} \div \sqrt{5 (0)}$

Step 3.2

The equation has an undefined fraction.

Undefined

Step 3.3

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

y-intercept(s): $None$

Step 4

List the intersections.

x-intercept(s): $None$

y-intercept(s): $None$

Step 5