Basic Math Examples

${(\frac{120 + 43}{0.35})}^{2} + \sqrt{3.8 \cdot 10^{- 4}}$

Step 1

Rewrite $\sqrt{3.8 \cdot 10^{- 4}}$ as $\sqrt{3.8} \cdot \sqrt{10^{- 4}}$ .

${(\frac{120 + 43}{0.35})}^{2} + \sqrt{3.8} \cdot \sqrt{10^{- 4}}$

Step 2

Evaluate the root.

${(\frac{120 + 43}{0.35})}^{2} + 1.94935886 \cdot \sqrt{10^{- 4}}$

Step 3

Rewrite $10^{- 4}$ as ${(10^{- 2})}^{2}$ .

${(\frac{120 + 43}{0.35})}^{2} + 1.94935886 \cdot \sqrt{{(10^{- 2})}^{2}}$

Step 4

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

${(\frac{120 + 43}{0.35})}^{2} + 1.94935886 \cdot 10^{- 2}$

Step 5

Simplify each term.

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Step 5.1

Add $120$ and $43$ .

${(\frac{163}{0.35})}^{2} + 1.94935886 \cdot 10^{- 2}$

Step 5.2

Divide $163$ by $0.35$ .

${465.\overline{714285}}^{2} + 1.94935886 \cdot 10^{- 2}$

Step 5.3

Raise $465.\overline{714285}$ to the power of $2$ .

$216889.79591836 + 1.94935886 \cdot 10^{- 2}$

Step 6

Convert $216889.79591836$ to scientific notation.

$2.16889795 \cdot 10^{5} + 1.94935886 \cdot 10^{- 2}$

Step 7

Move the decimal point in $1.94935886$ to the left by $7$ places and increase the power of $10^{- 2}$ by $7$ .

$2.16889795 \cdot 10^{5} + 0.00000019 \cdot 10^{5}$

Step 8

Factor $10^{5}$ out of $2.16889795 \cdot 10^{5} + 0.00000019 \cdot 10^{5}$ .

$(2.16889795 + 0.00000019) \cdot 10^{5}$

Step 9

Add $2.16889795$ and $0.00000019$ .

$2.16889815 \cdot 10^{5}$

Step 10

The result can be shown in multiple forms.

Scientific Notation:

$2.16889815 \cdot 10^{5}$

Expanded Form:

$216889.81541195$