Basic Math Examples

$84 = 2 \cdot (14 \sqrt{l \div 2.3})$

Step 1

Rewrite the equation as $2 \cdot (14 \sqrt{l \div 2.3}) = 84$ .

$2 \cdot (14 \sqrt{l \div 2.3}) = 84$

Step 2

Multiply $14$ by $2$ .

$28 \cdot \sqrt{l \div 2.3} = 84$

Step 3

Divide each term in $28 \cdot \sqrt{l \div 2.3} = 84$ by $28$ and simplify.

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Step 3.1

Divide each term in $28 \cdot \sqrt{l \div 2.3} = 84$ by $28$ .

$\frac{28 \cdot \sqrt{l \div 2.3}}{28} = \frac{84}{28}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $28$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{28 \cdot \sqrt{l \div 2.3}}{28} = \frac{84}{28}$

Step 3.2.1.2

Divide $\sqrt{l \div 2.3}$ by $1$ .

$\sqrt{l \div 2.3} = \frac{84}{28}$

Step 3.2.2

Rewrite the division as a fraction.

$\sqrt{\frac{l}{2.3}} = \frac{84}{28}$

Step 3.2.3

Multiply by $1$ .

$\sqrt{\frac{1 l}{2.3}} = \frac{84}{28}$

Step 3.2.4

Factor $2.3$ out of $2.3$ .

$\sqrt{\frac{1 l}{2.3 (1)}} = \frac{84}{28}$

Step 3.2.5

Separate fractions.

$\sqrt{\frac{1}{2.3} \cdot \frac{l}{1}} = \frac{84}{28}$

Step 3.2.6

Divide $1$ by $2.3$ .

$\sqrt{0.4347826 \frac{l}{1}} = \frac{84}{28}$

Step 3.2.7

Divide $l$ by $1$ .

$\sqrt{0.4347826 l} = \frac{84}{28}$

Step 3.2.8

Rewrite $0.4347826 l$ as ${({0.81202245}^{2})}^{2} l$ .

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Step 3.2.8.1

Rewrite $0.4347826$ as ${0.65938047}^{2}$ .

$\sqrt{{0.65938047}^{2} l} = \frac{84}{28}$

Step 3.2.8.2

Rewrite $0.65938047$ as ${0.81202245}^{2}$ .

$\sqrt{{({0.81202245}^{2})}^{2} l} = \frac{84}{28}$

Step 3.2.9

Pull terms out from under the radical.

${0.81202245}^{2} \sqrt{l} = \frac{84}{28}$

Step 3.2.10

Raise $0.81202245$ to the power of $2$ .

$0.65938047 \sqrt{l} = \frac{84}{28}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $84$ by $28$ .

$0.65938047 \sqrt{l} = 3$

Step 4

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

${(0.65938047 \sqrt{l})}^{2} = 3^{2}$

Step 5

Simplify each side of the equation.

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Step 5.1

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

${(0.65938047 l^{\frac{1}{2}})}^{2} = 3^{2}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Simplify ${(0.65938047 l^{\frac{1}{2}})}^{2}$ .

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Step 5.2.1.1

Apply the product rule to $0.65938047 l^{\frac{1}{2}}$ .

${0.65938047}^{2} {(l^{\frac{1}{2}})}^{2} = 3^{2}$

Step 5.2.1.2

Raise $0.65938047$ to the power of $2$ .

$0.4347826 {(l^{\frac{1}{2}})}^{2} = 3^{2}$

Step 5.2.1.3

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

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Step 5.2.1.3.1

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

$0.4347826 l^{\frac{1}{2} \cdot 2} = 3^{2}$

Step 5.2.1.3.2

Cancel the common factor of $2$ .

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Step 5.2.1.3.2.1

Cancel the common factor.

$0.4347826 l^{\frac{1}{2} \cdot 2} = 3^{2}$

Step 5.2.1.3.2.2

Rewrite the expression.

$0.4347826 l^{1} = 3^{2}$

Step 5.2.1.4

Simplify.

$0.4347826 l = 3^{2}$

Step 5.3

Simplify the right side.

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Step 5.3.1

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

$0.4347826 l = 9$

Step 6

Divide each term in $0.4347826 l = 9$ by $0.4347826$ and simplify.

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Step 6.1

Divide each term in $0.4347826 l = 9$ by $0.4347826$ .

$\frac{0.4347826 l}{0.4347826} = \frac{9}{0.4347826}$

Step 6.2

Simplify the left side.

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Step 6.2.1

Cancel the common factor of $0.4347826$ .

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Step 6.2.1.1

Cancel the common factor.

$\frac{0.4347826 l}{0.4347826} = \frac{9}{0.4347826}$

Step 6.2.1.2

Divide $l$ by $1$ .

$l = \frac{9}{0.4347826}$

Step 6.3

Simplify the right side.

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Step 6.3.1

Divide $9$ by $0.4347826$ .

$l = 20.7$