Simplify the Radical Expression 0.04 square root of 72+0.05 square root of 98-1/5 square root of 50

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

Simplify each term.

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

Factor $36$ out of $72$ .

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

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

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

Pull terms out from under the radical.

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

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

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

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

Multiply $6$ by $0.04$ .

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

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

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

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

Factor $49$ out of $98$ .

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

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

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

Pull terms out from under the radical.

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

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

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

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

Multiply $7$ by $0.05$ .

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

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

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

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

Factor $25$ out of $50$ .

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

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

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

Pull terms out from under the radical.

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

Remove non-negative terms from the absolute value.

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

Cancel the common factor of $5$ .

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

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

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

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

Cancel the common factor.

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

Rewrite the expression.

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

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

$0.33941125 + 0.49497474 - \sqrt{2}$

Add $0.33941125$ and $0.49497474$ .

$0.834386 - \sqrt{2}$

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

$- 0.57982756$

Simplify the Radical Expression 0.04 square root of 72+0.05 square root of 98-1/5 square root of 50

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