Basic Math Examples

$b m i = 703 \cdot 148 \div h^{2}$

Step 1

Rewrite the equation as $703 \cdot 148 \div h^{2} = b m i$ .

$703 \cdot 148 \div h^{2} = b m i$

Step 2

Multiply both sides by $h^{2}$ .

$703 \cdot 148 \div h^{2} h^{2} = b m i h^{2}$

Step 3

Simplify the left side.

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Step 3.1

Simplify $703 \cdot 148 \div h^{2} h^{2}$ .

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Step 3.1.1

Rewrite the division as a fraction.

$\frac{703 \cdot 148}{h^{2}} h^{2} = b m i h^{2}$

Step 3.1.2

Cancel the common factor of $h^{2}$ .

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Step 3.1.2.1

Cancel the common factor.

$\frac{703 \cdot 148}{h^{2}} h^{2} = b m i h^{2}$

Step 3.1.2.2

Rewrite the expression.

$703 \cdot 148 = b m i h^{2}$

Step 3.1.3

Multiply $703$ by $148$ .

$104044 = b m i h^{2}$

Step 4

Solve for $h$ .

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Step 4.1

Rewrite the equation as $b m i h^{2} = 104044$ .

$b m i h^{2} = 104044$

Step 4.2

Divide each term in $b m i h^{2} = 104044$ by $b m i$ and simplify.

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Step 4.2.1

Divide each term in $b m i h^{2} = 104044$ by $b m i$ .

$\frac{b m i h^{2}}{b m i} = \frac{104044}{b m i}$

Step 4.2.2

Simplify the left side.

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Step 4.2.2.1

Cancel the common factor of $b$ .

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Step 4.2.2.1.1

Cancel the common factor.

$\frac{b m i h^{2}}{b m i} = \frac{104044}{b m i}$

Step 4.2.2.1.2

Rewrite the expression.

$\frac{m i h^{2}}{m i} = \frac{104044}{b m i}$

Step 4.2.2.2

Cancel the common factor of $m$ .

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Step 4.2.2.2.1

Cancel the common factor.

$\frac{m i h^{2}}{m i} = \frac{104044}{b m i}$

Step 4.2.2.2.2

Rewrite the expression.

$\frac{i h^{2}}{i} = \frac{104044}{b m i}$

Step 4.2.2.3

Cancel the common factor of $i$ .

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Step 4.2.2.3.1

Cancel the common factor.

$\frac{i h^{2}}{i} = \frac{104044}{b m i}$

Step 4.2.2.3.2

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

$h^{2} = \frac{104044}{b m i}$

Step 4.3

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

$h = \pm \sqrt{\frac{104044}{b m i}}$

Step 4.4

Simplify $\pm \sqrt{\frac{104044}{b m i}}$ .

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Step 4.4.1

Rewrite $\sqrt{\frac{104044}{b m i}}$ as $\frac{\sqrt{104044}}{\sqrt{b m i}}$ .

$h = \pm \frac{\sqrt{104044}}{\sqrt{b m i}}$

Step 4.4.2

Simplify the numerator.

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Step 4.4.2.1

Rewrite $104044$ as $74^{2} \cdot 19$ .

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Step 4.4.2.1.1

Factor $5476$ out of $104044$ .

$h = \pm \frac{\sqrt{5476 (19)}}{\sqrt{b m i}}$

Step 4.4.2.1.2

Rewrite $5476$ as $74^{2}$ .

$h = \pm \frac{\sqrt{74^{2} \cdot 19}}{\sqrt{b m i}}$

Step 4.4.2.2

Pull terms out from under the radical.

$h = \pm \frac{74 \sqrt{19}}{\sqrt{b m i}}$

Step 4.4.3

Multiply $\frac{74 \sqrt{19}}{\sqrt{b m i}}$ by $\frac{\sqrt{b m i}}{\sqrt{b m i}}$ .

$h = \pm \frac{74 \sqrt{19}}{\sqrt{b m i}} \cdot \frac{\sqrt{b m i}}{\sqrt{b m i}}$

Step 4.4.4

Combine and simplify the denominator.

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Step 4.4.4.1

Multiply $\frac{74 \sqrt{19}}{\sqrt{b m i}}$ by $\frac{\sqrt{b m i}}{\sqrt{b m i}}$ .

$h = \pm \frac{74 \sqrt{19} \sqrt{b m i}}{\sqrt{b m i} \sqrt{b m i}}$

Step 4.4.4.2

Raise $\sqrt{b m i}$ to the power of $1$ .

$h = \pm \frac{74 \sqrt{19} \sqrt{b m i}}{{\sqrt{b m i}}^{1} \sqrt{b m i}}$

Step 4.4.4.3

Raise $\sqrt{b m i}$ to the power of $1$ .

$h = \pm \frac{74 \sqrt{19} \sqrt{b m i}}{{\sqrt{b m i}}^{1} {\sqrt{b m i}}^{1}}$

Step 4.4.4.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$h = \pm \frac{74 \sqrt{19} \sqrt{b m i}}{{\sqrt{b m i}}^{1 + 1}}$

Step 4.4.4.5

Add $1$ and $1$ .

$h = \pm \frac{74 \sqrt{19} \sqrt{b m i}}{{\sqrt{b m i}}^{2}}$

Step 4.4.4.6

Rewrite ${\sqrt{b m i}}^{2}$ as $b m i$ .

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Step 4.4.4.6.1

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

$h = \pm \frac{74 \sqrt{19} \sqrt{b m i}}{{({(b m i)}^{\frac{1}{2}})}^{2}}$

Step 4.4.4.6.2

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

$h = \pm \frac{74 \sqrt{19} \sqrt{b m i}}{{(b m i)}^{\frac{1}{2} \cdot 2}}$

Step 4.4.4.6.3

Combine $\frac{1}{2}$ and $2$ .

$h = \pm \frac{74 \sqrt{19} \sqrt{b m i}}{{(b m i)}^{\frac{2}{2}}}$

Step 4.4.4.6.4

Cancel the common factor of $2$ .

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Step 4.4.4.6.4.1

Cancel the common factor.

$h = \pm \frac{74 \sqrt{19} \sqrt{b m i}}{{(b m i)}^{\frac{2}{2}}}$

Step 4.4.4.6.4.2

Rewrite the expression.

$h = \pm \frac{74 \sqrt{19} \sqrt{b m i}}{{(b m i)}^{1}}$

Step 4.4.4.6.5

Simplify.

$h = \pm \frac{74 \sqrt{19} \sqrt{b m i}}{b m i}$

Step 4.4.5

Combine using the product rule for radicals.

$h = \pm \frac{74 \sqrt{b m i \cdot 19}}{b m i}$

Step 4.4.6

Move $19$ to the left of $b m i$ .

$h = \pm \frac{74 \sqrt{19 b m i}}{b m i}$

Step 4.5

The complete solution is the result of both the positive and negative portions of the solution.

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Step 4.5.1

First, use the positive value of the $\pm$ to find the first solution.

$h = \frac{74 \sqrt{19 b m i}}{b m i}$

Step 4.5.2

Next, use the negative value of the $\pm$ to find the second solution.

$h = - \frac{74 \sqrt{19 b m i}}{b m i}$

Step 4.5.3

The complete solution is the result of both the positive and negative portions of the solution.

$h = \frac{74 \sqrt{19 b m i}}{b m i}$

$h = - \frac{74 \sqrt{19 b m i}}{b m i}$

$h = \frac{74 \sqrt{19 b m i}}{b m i}$

$h = - \frac{74 \sqrt{19 b m i}}{b m i}$

$h = \frac{74 \sqrt{19 b m i}}{b m i}$

$h = - \frac{74 \sqrt{19 b m i}}{b m i}$