Basic Math Examples

$\frac{\sqrt{(9 \times 10^{9}) (0.000037) (0.000038)}}{31^{2}}$

Step 1

Convert $0.000037$ to scientific notation.

$\frac{\sqrt{9 \cdot 10^{9} \cdot 3.7 \cdot 10^{- 5} \cdot 0.000038}}{31^{2}}$

Step 2

Multiply $9$ by $3.7$ .

$\frac{\sqrt{33.3 (10^{9} \cdot 10^{- 5}) \cdot 0.000038}}{31^{2}}$

Step 3

Multiply $10^{9}$ by $10^{- 5}$ by adding the exponents.

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Step 3.1

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

$\frac{\sqrt{33.3 \cdot 10^{9 - 5} \cdot 0.000038}}{31^{2}}$

Step 3.2

Subtract $5$ from $9$ .

$\frac{\sqrt{33.3 \cdot 10^{4} \cdot 0.000038}}{31^{2}}$

Step 4

Convert $0.000038$ to scientific notation.

$\frac{\sqrt{33.3 \cdot 10^{4} \cdot 3.8 \cdot 10^{- 5}}}{31^{2}}$

Step 5

Multiply $33.3$ by $3.8$ .

$\frac{\sqrt{126.54 (10^{4} \cdot 10^{- 5})}}{31^{2}}$

Step 6

Multiply $10^{4}$ by $10^{- 5}$ by adding the exponents.

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Step 6.1

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

$\frac{\sqrt{126.54 \cdot 10^{4 - 5}}}{31^{2}}$

Step 6.2

Subtract $5$ from $4$ .

$\frac{\sqrt{126.54 \cdot 10^{- 1}}}{31^{2}}$

Step 7

Rewrite $126.54 \cdot 10^{- 1}$ as $12.654 \cdot 10^{0}$ .

$\frac{\sqrt{12.654 \cdot 10^{0}}}{31^{2}}$

Step 8

Rewrite $\sqrt{12.654 \cdot 10^{0}}$ as $\sqrt{12.654} \cdot \sqrt{10^{0}}$ .

$\frac{\sqrt{12.654} \cdot \sqrt{10^{0}}}{31^{2}}$

Step 9

Evaluate the root.

$\frac{3.55724612 \cdot \sqrt{10^{0}}}{31^{2}}$

Step 10

Rewrite $10^{0}$ as ${(10^{0})}^{2}$ .

$\frac{3.55724612 \cdot \sqrt{{(10^{0})}^{2}}}{31^{2}}$

Step 11

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

$\frac{3.55724612 \cdot 10^{0}}{31^{2}}$

Step 12

Convert $3.55724612 \cdot 10^{0}$ from scientific notation.

$\frac{3.55724612}{31^{2}}$

Step 13

Raise $31$ to the power of $2$ .

$\frac{3.55724612}{961}$

Step 14

Divide $3.55724612$ by $961$ .

$0.0037016$