Calculus Examples

${(1140 - 19 l)}^{\frac{1}{2}} \cdot l^{\frac{1}{2}} = 0$

Step 1

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

${(1140 - 19 l)}^{\frac{1}{2}} = 0$

$l^{\frac{1}{2}} = 0$

Step 2

Set ${(1140 - 19 l)}^{\frac{1}{2}}$ equal to $0$ and solve for $l$ .

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Step 2.1

Set ${(1140 - 19 l)}^{\frac{1}{2}}$ equal to $0$ .

${(1140 - 19 l)}^{\frac{1}{2}} = 0$

Step 2.2

Solve ${(1140 - 19 l)}^{\frac{1}{2}} = 0$ for $l$ .

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Step 2.2.1

Set the $1140 - 19 l$ equal to $0$ .

$1140 - 19 l = 0$

Step 2.2.2

Solve for $l$ .

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Step 2.2.2.1

Subtract $1140$ from both sides of the equation.

$- 19 l = - 1140$

Step 2.2.2.2

Divide each term in $- 19 l = - 1140$ by $- 19$ and simplify.

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Step 2.2.2.2.1

Divide each term in $- 19 l = - 1140$ by $- 19$ .

$\frac{- 19 l}{- 19} = \frac{- 1140}{- 19}$

Step 2.2.2.2.2

Simplify the left side.

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Step 2.2.2.2.2.1

Cancel the common factor of $- 19$ .

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Step 2.2.2.2.2.1.1

Cancel the common factor.

$\frac{- 19 l}{- 19} = \frac{- 1140}{- 19}$

Step 2.2.2.2.2.1.2

Divide $l$ by $1$ .

$l = \frac{- 1140}{- 19}$

Step 2.2.2.2.3

Simplify the right side.

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Step 2.2.2.2.3.1

Divide $- 1140$ by $- 19$ .

$l = 60$

Step 3

Set $l^{\frac{1}{2}}$ equal to $0$ and solve for $l$ .

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Step 3.1

Set $l^{\frac{1}{2}}$ equal to $0$ .

$l^{\frac{1}{2}} = 0$

Step 3.2

Solve $l^{\frac{1}{2}} = 0$ for $l$ .

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Step 3.2.1

Raise each side of the equation to the power of $2$ to eliminate the fractional exponent on the left side.

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

Step 3.2.2

Simplify the exponent.

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Step 3.2.2.1

Simplify the left side.

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Step 3.2.2.1.1

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

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Step 3.2.2.1.1.1

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

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Step 3.2.2.1.1.1.1

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

$l^{\frac{1}{2} \cdot 2} = 0^{2}$

Step 3.2.2.1.1.1.2

Cancel the common factor of $2$ .

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Step 3.2.2.1.1.1.2.1

Cancel the common factor.

$l^{\frac{1}{2} \cdot 2} = 0^{2}$

Step 3.2.2.1.1.1.2.2

Rewrite the expression.

$l^{1} = 0^{2}$

Step 3.2.2.1.1.2

Simplify.

$l = 0^{2}$

Step 3.2.2.2

Simplify the right side.

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Step 3.2.2.2.1

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

$l = 0$

Step 4

The final solution is all the values that make ${(1140 - 19 l)}^{\frac{1}{2}} \cdot l^{\frac{1}{2}} = 0$ true.

$l = 60, 0$