simplify |3sqrt(2)-2|+|4-3sqrt(2)|

1) Let's reduce:

| 3 \times \sqrt{2} - 2 | + | 4 - 3 \times \sqrt{2} |

2) Let's examine the sign of:

3 \times \sqrt{2} - 2

3 \times \approx 1.4142 - 2

\approx 4.2426 - 2

\approx 2.2426

Here the argument of abs ≥ 0, so abs disappears

3) Let's examine the sign of:

4 - 3 \times \sqrt{2}

4 - 3 \times \approx 1.4142

4 - \approx 4.2426

\approx -0.2426

Here the argument of abs ≤ 0, so we take its opposite

ⓘ The expression inside the absolute value is nonpositive, so its absolute value equals its opposite:

| 4 - 3 \times \sqrt{2} |

- (4 - 3 \times \sqrt{2})

3 \times \sqrt{2} - 2 - (4 - 3 \times \sqrt{2})

ⓘ A minus sign before a parenthesis changes the sign of each of its terms:

- (4 - 3 \times \sqrt{2})

- 4 + 3 \times \sqrt{2}

3 \times \sqrt{2}

- 2

- 4

+ 3 \times \sqrt{2}

ⓘ Start from

-2

and move back

4

more on the number line, away from zero:

- 2 - 4

-6

■Like terms are grouped by adding their coefficients:

3 \times \sqrt{2} + 3 \times \sqrt{2}

6 \times \sqrt{2}

▶Simplified form:

6 \times \sqrt{2} - 6

4) The numeric value of:

6 \times \sqrt{2} - 6

is:

6 \times \approx 1.4142 - 6

\approx 8.4853 - 6

▷

\approx 2.4853