Basic Math Examples

$\sqrt[3]{7 + 4 \cdot 5} + 9^{2} \div 3^{2} - \sqrt{100 + 7 \cdot 3}$

Step 1

Find the common denominator.

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Step 1.1

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

$\sqrt[3]{7 + 4 \cdot 5} + 9^{2} \div 9 - \sqrt{100 + 7 \cdot 3}$

Step 1.2

Write $\sqrt[3]{7 + 4 \cdot 5}$ as a fraction with denominator $1$ .

$\frac{\sqrt[3]{7 + 4 \cdot 5}}{1} + 9^{2} \div 9 - \sqrt{100 + 7 \cdot 3}$

Step 1.3

Multiply $\frac{\sqrt[3]{7 + 4 \cdot 5}}{1}$ by $\frac{9}{9}$ .

$\frac{\sqrt[3]{7 + 4 \cdot 5}}{1} \cdot \frac{9}{9} + 9^{2} \div 9 - \sqrt{100 + 7 \cdot 3}$

Step 1.4

Multiply $\frac{\sqrt[3]{7 + 4 \cdot 5}}{1}$ by $\frac{9}{9}$ .

$\frac{\sqrt[3]{7 + 4 \cdot 5} \cdot 9}{9} + 9^{2} \div 9 - \sqrt{100 + 7 \cdot 3}$

Step 1.5

Write $- \sqrt{100 + 7 \cdot 3}$ as a fraction with denominator $1$ .

$\frac{\sqrt[3]{7 + 4 \cdot 5} \cdot 9}{9} + 9^{2} \div 9 + \frac{- \sqrt{100 + 7 \cdot 3}}{1}$

Step 1.6

Multiply $\frac{- \sqrt{100 + 7 \cdot 3}}{1}$ by $\frac{9}{9}$ .

$\frac{\sqrt[3]{7 + 4 \cdot 5} \cdot 9}{9} + 9^{2} \div 9 + \frac{- \sqrt{100 + 7 \cdot 3}}{1} \cdot \frac{9}{9}$

Step 1.7

Multiply $\frac{- \sqrt{100 + 7 \cdot 3}}{1}$ by $\frac{9}{9}$ .

$\frac{\sqrt[3]{7 + 4 \cdot 5} \cdot 9}{9} + 9^{2} \div 9 + \frac{- \sqrt{100 + 7 \cdot 3} \cdot 9}{9}$

Step 2

Combine the numerators over the common denominator.

$\frac{\sqrt[3]{7 + 4 \cdot 5} \cdot 9 + 9^{2} - \sqrt{100 + 7 \cdot 3} \cdot 9}{9}$

Step 3

Simplify each term.

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Step 3.1

Multiply $4$ by $5$ .

$\frac{\sqrt[3]{7 + 20} \cdot 9 + 9^{2} - \sqrt{100 + 7 \cdot 3} \cdot 9}{9}$

Step 3.2

Add $7$ and $20$ .

$\frac{\sqrt[3]{27} \cdot 9 + 9^{2} - \sqrt{100 + 7 \cdot 3} \cdot 9}{9}$

Step 3.3

Rewrite $27$ as $3^{3}$ .

$\frac{\sqrt[3]{3^{3}} \cdot 9 + 9^{2} - \sqrt{100 + 7 \cdot 3} \cdot 9}{9}$

Step 3.4

Pull terms out from under the radical, assuming real numbers.

$\frac{3 \cdot 9 + 9^{2} - \sqrt{100 + 7 \cdot 3} \cdot 9}{9}$

Step 3.5

Multiply $3$ by $9$ .

$\frac{27 + 9^{2} - \sqrt{100 + 7 \cdot 3} \cdot 9}{9}$

Step 3.6

Raise $9$ to the power of $2$ .

$\frac{27 + 81 - \sqrt{100 + 7 \cdot 3} \cdot 9}{9}$

Step 3.7

Multiply $7$ by $3$ .

$\frac{27 + 81 - \sqrt{100 + 21} \cdot 9}{9}$

Step 3.8

Add $100$ and $21$ .

$\frac{27 + 81 - \sqrt{121} \cdot 9}{9}$

Step 3.9

Rewrite $121$ as $11^{2}$ .

$\frac{27 + 81 - \sqrt{11^{2}} \cdot 9}{9}$

Step 3.10

Pull terms out from under the radical, assuming positive real numbers.

$\frac{27 + 81 - 1 \cdot 11 \cdot 9}{9}$

Step 3.11

Multiply $- 1 \cdot 11 \cdot 9$ .

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Step 3.11.1

Multiply $- 1$ by $11$ .

$\frac{27 + 81 - 11 \cdot 9}{9}$

Step 3.11.2

Multiply $- 11$ by $9$ .

$\frac{27 + 81 - 99}{9}$

Step 4

Simplify the expression.

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Step 4.1

Add $27$ and $81$ .

$\frac{108 - 99}{9}$

Step 4.2

Subtract $99$ from $108$ .

$\frac{9}{9}$

Step 4.3

Divide $9$ by $9$ .

$1$