Basic Math Examples

${(\sqrt{m \cdot 30})}^{2} + m \cdot 30 \div 3 \cdot m$

Step 1

Rewrite ${\sqrt{m \cdot 30}}^{2}$ as $m \cdot 30$ .

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Step 1.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{m \cdot 30}$ as ${(m \cdot 30)}^{\frac{1}{2}}$ .

${({(m \cdot 30)}^{\frac{1}{2}})}^{2} + m \cdot 30 \div 3 \cdot m$

Step 1.2

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

${(m \cdot 30)}^{\frac{1}{2} \cdot 2} + m \cdot 30 \div 3 \cdot m$

Step 1.3

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

${(m \cdot 30)}^{\frac{2}{2}} + m \cdot 30 \div 3 \cdot m$

Step 1.4

Cancel the common factor of $2$ .

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Step 1.4.1

Cancel the common factor.

${(m \cdot 30)}^{\frac{2}{2}} + m \cdot 30 \div 3 \cdot m$

Step 1.4.2

Rewrite the expression.

${(m \cdot 30)}^{1} + m \cdot 30 \div 3 \cdot m$

Step 1.5

Simplify.

$m \cdot 30 + m \cdot 30 \div 3 \cdot m$

Step 2

Move $30$ to the left of $m$ .

$30 \cdot m + m \cdot 30 \div 3 \cdot m$

Step 3

Rewrite the division as a fraction.

$30 m + \frac{m \cdot 30}{3} \cdot m$

Step 4

Cancel the common factor of $30$ and $3$ .

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Step 4.1

Factor $3$ out of $m \cdot 30$ .

$30 m + \frac{3 (m \cdot 10)}{3} \cdot m$

Step 4.2

Cancel the common factors.

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Step 4.2.1

Factor $3$ out of $3$ .

$30 m + \frac{3 (m \cdot 10)}{3 (1)} \cdot m$

Step 4.2.2

Cancel the common factor.

$30 m + \frac{3 (m \cdot 10)}{3 \cdot 1} \cdot m$

Step 4.2.3

Rewrite the expression.

$30 m + \frac{m \cdot 10}{1} \cdot m$

Step 4.2.4

Divide $m \cdot 10$ by $1$ .

$30 m + m \cdot 10 \cdot m$

Step 5

Multiply $m$ by $m$ by adding the exponents.

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Step 5.1

Move $m$ .

$30 m + m \cdot m \cdot 10$

Step 5.2

Multiply $m$ by $m$ .

$30 m + m^{2} \cdot 10$

Step 6

Move $10$ to the left of $m^{2}$ .

$30 m + 10 m^{2}$