Basic Math Examples

$- 3 \sqrt{2 v} = 18$

Step 1

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

${(- 3 \sqrt{2 v})}^{2} = 18^{2}$

Step 2

Simplify each side of the equation.

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Step 2.1

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

${(- 3 {(2 v)}^{\frac{1}{2}})}^{2} = 18^{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify ${(- 3 {(2 v)}^{\frac{1}{2}})}^{2}$ .

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Step 2.2.1.1

Apply the product rule to $2 v$ .

${(- 3 (2^{\frac{1}{2}} v^{\frac{1}{2}}))}^{2} = 18^{2}$

Step 2.2.1.2

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Step 2.2.1.2.1

Apply the product rule to $- 3 \cdot 2^{\frac{1}{2}} v^{\frac{1}{2}}$ .

${(- 3 \cdot 2^{\frac{1}{2}})}^{2} {(v^{\frac{1}{2}})}^{2} = 18^{2}$

Step 2.2.1.2.2

Apply the product rule to $- 3 \cdot 2^{\frac{1}{2}}$ .

${(- 3)}^{2} \cdot {(2^{\frac{1}{2}})}^{2} {(v^{\frac{1}{2}})}^{2} = 18^{2}$

Step 2.2.1.3

Raise $- 3$ to the power of $2$ .

$9 \cdot {(2^{\frac{1}{2}})}^{2} {(v^{\frac{1}{2}})}^{2} = 18^{2}$

Step 2.2.1.4

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

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Step 2.2.1.4.1

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

$9 \cdot 2^{\frac{1}{2} \cdot 2} {(v^{\frac{1}{2}})}^{2} = 18^{2}$

Step 2.2.1.4.2

Cancel the common factor of $2$ .

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Step 2.2.1.4.2.1

Cancel the common factor.

$9 \cdot 2^{\frac{1}{2} \cdot 2} {(v^{\frac{1}{2}})}^{2} = 18^{2}$

Step 2.2.1.4.2.2

Rewrite the expression.

$9 \cdot 2^{1} {(v^{\frac{1}{2}})}^{2} = 18^{2}$

Step 2.2.1.5

Evaluate the exponent.

$9 \cdot 2 {(v^{\frac{1}{2}})}^{2} = 18^{2}$

Step 2.2.1.6

Multiply $9$ by $2$ .

$18 {(v^{\frac{1}{2}})}^{2} = 18^{2}$

Step 2.2.1.7

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

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Step 2.2.1.7.1

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

$18 v^{\frac{1}{2} \cdot 2} = 18^{2}$

Step 2.2.1.7.2

Cancel the common factor of $2$ .

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Step 2.2.1.7.2.1

Cancel the common factor.

$18 v^{\frac{1}{2} \cdot 2} = 18^{2}$

Step 2.2.1.7.2.2

Rewrite the expression.

$18 v^{1} = 18^{2}$

Step 2.2.1.8

Simplify.

$18 v = 18^{2}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Raise $18$ to the power of $2$ .

$18 v = 324$

Step 3

Divide each term in $18 v = 324$ by $18$ and simplify.

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Step 3.1

Divide each term in $18 v = 324$ by $18$ .

$\frac{18 v}{18} = \frac{324}{18}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $18$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{18 v}{18} = \frac{324}{18}$

Step 3.2.1.2

Divide $v$ by $1$ .

$v = \frac{324}{18}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $324$ by $18$ .

$v = 18$

Step 4

Exclude the solutions that do not make $- 3 \sqrt{2 v} = 18$ true.

$No solution$