Algebra Examples

$0.04 \sqrt{72} + 0.05 \sqrt{98} - \frac{1}{5} \sqrt{50}$

Step 1

Simplify each term.

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Step 1.1

Rewrite $72$ as $6^{2} \cdot 2$ .

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Step 1.1.1

Factor $36$ out of $72$ .

$0.04 \sqrt{36 (2)} + 0.05 \sqrt{98} - \frac{1}{5} \sqrt{50}$

Step 1.1.2

Rewrite $36$ as $6^{2}$ .

$0.04 \sqrt{6^{2} \cdot 2} + 0.05 \sqrt{98} - \frac{1}{5} \sqrt{50}$

Step 1.2

Pull terms out from under the radical.

$0.04 (| 6 | \sqrt{2}) + 0.05 \sqrt{98} - \frac{1}{5} \sqrt{50}$

Step 1.3

The absolute value is the distance between a number and zero. The distance between $0$ and $6$ is $6$ .

$0.04 (6 \sqrt{2}) + 0.05 \sqrt{98} - \frac{1}{5} \sqrt{50}$

Step 1.4

Multiply $0.04 (6 \sqrt{2})$ .

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Step 1.4.1

Multiply $6$ by $0.04$ .

$0.24 \sqrt{2} + 0.05 \sqrt{98} - \frac{1}{5} \sqrt{50}$

Step 1.4.2

Multiply $0.24$ by $\sqrt{2}$ .

$0.33941125 + 0.05 \sqrt{98} - \frac{1}{5} \sqrt{50}$

Step 1.5

Rewrite $98$ as $7^{2} \cdot 2$ .

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Step 1.5.1

Factor $49$ out of $98$ .

$0.33941125 + 0.05 \sqrt{49 (2)} - \frac{1}{5} \sqrt{50}$

Step 1.5.2

Rewrite $49$ as $7^{2}$ .

$0.33941125 + 0.05 \sqrt{7^{2} \cdot 2} - \frac{1}{5} \sqrt{50}$

Step 1.6

Pull terms out from under the radical.

$0.33941125 + 0.05 (| 7 | \sqrt{2}) - \frac{1}{5} \sqrt{50}$

Step 1.7

The absolute value is the distance between a number and zero. The distance between $0$ and $7$ is $7$ .

$0.33941125 + 0.05 (7 \sqrt{2}) - \frac{1}{5} \sqrt{50}$

Step 1.8

Multiply $0.05 (7 \sqrt{2})$ .

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Step 1.8.1

Multiply $7$ by $0.05$ .

$0.33941125 + 0.35 \sqrt{2} - \frac{1}{5} \sqrt{50}$

Step 1.8.2

Multiply $0.35$ by $\sqrt{2}$ .

$0.33941125 + 0.49497474 - \frac{1}{5} \sqrt{50}$

Step 1.9

Rewrite $50$ as $5^{2} \cdot 2$ .

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Step 1.9.1

Factor $25$ out of $50$ .

$0.33941125 + 0.49497474 - \frac{1}{5} \sqrt{25 (2)}$

Step 1.9.2

Rewrite $25$ as $5^{2}$ .

$0.33941125 + 0.49497474 - \frac{1}{5} \sqrt{5^{2} \cdot 2}$

Step 1.10

Pull terms out from under the radical.

$0.33941125 + 0.49497474 - \frac{1}{5} (| 5 | \sqrt{2})$

Step 1.11

Remove non-negative terms from the absolute value.

$0.33941125 + 0.49497474 - \frac{1}{5} (5 \sqrt{2})$

Step 1.12

Cancel the common factor of $5$ .

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Step 1.12.1

Move the leading negative in $- \frac{1}{5}$ into the numerator.

$0.33941125 + 0.49497474 + \frac{- 1}{5} (5 \sqrt{2})$

Step 1.12.2

Factor $5$ out of $5 \sqrt{2}$ .

$0.33941125 + 0.49497474 + \frac{- 1}{5} (5 (\sqrt{2}))$

Step 1.12.3

Cancel the common factor.

$0.33941125 + 0.49497474 + \frac{- 1}{5} (5 \sqrt{2})$

Step 1.12.4

Rewrite the expression.

$0.33941125 + 0.49497474 - 1 \sqrt{2}$

Step 1.13

Rewrite $- 1 \sqrt{2}$ as $- \sqrt{2}$ .

$0.33941125 + 0.49497474 - \sqrt{2}$

Step 2

Add $0.33941125$ and $0.49497474$ .

$0.834386 - \sqrt{2}$

Step 3

Subtract $\sqrt{2}$ from $0.834386$ .

$- 0.57982756$