Evaluate square root of ((9*10^9)(0.000037)(0.000038))/31

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

Step 1

Convert $0.000037$ to scientific notation.

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

Step 2

Multiply $9$ by $3.7$ .

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

Step 3

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

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

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

Subtract $5$ from $9$ .

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

Step 4

Convert $0.000038$ to scientific notation.

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

Step 5

Multiply $33.3$ by $3.8$ .

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

Step 6

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

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

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

Subtract $5$ from $4$ .

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

Step 7

Divide using scientific notation.

Group coefficients together and exponents together to divide numbers in scientific notation.

$\sqrt{(\frac{126.54}{31}) (\frac{10^{- 1}}{1})}$

Divide $126.54$ by $31$ .

$\sqrt{4.08193548 \frac{10^{- 1}}{1}}$

Divide $10^{- 1}$ by $1$ .

$\sqrt{4.08193548 \cdot 10^{- 1}}$

Step 8

Rewrite $4.08193548 \cdot 10^{- 1}$ as $0.40819354 \cdot 10^{0}$ .

$\sqrt{0.40819354 \cdot 10^{0}}$

Step 9

Rewrite $\sqrt{0.40819354 \cdot 10^{0}}$ as $\sqrt{0.40819354} \cdot \sqrt{10^{0}}$ .

$\sqrt{0.40819354} \cdot \sqrt{10^{0}}$

Step 10

Evaluate the root.

$0.63890026 \cdot \sqrt{10^{0}}$

Step 11

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

$0.63890026 \cdot \sqrt{{(10^{0})}^{2}}$

Step 12

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

$0.63890026 \cdot 10^{0}$

Step 13

Move the decimal point in $0.63890026$ to the right by $1$ place and decrease the power of $10^{0}$ by $1$ .

$6.38900264 \cdot 10^{- 1}$

Step 14

The result can be shown in multiple forms.

Scientific Notation:

$6.38900264 \cdot 10^{- 1}$

Expanded Form:

$0.63890026$

Evaluate square root of ((9*10^9)(0.000037)(0.000038))/31

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