simplify 2sqrt(20)-sqrt(20)+3sqrt(20)-2sqrt(45)

Let's simplify:

2 \times \sqrt{20}

- \sqrt{20}

+ 3 \times \sqrt{20}

- 2 \times \sqrt{45}

ⓘ We look for the largest square dividing

20

4

2^{2}

, and take it out of the root:

\sqrt{20}

\sqrt{4 \times 5}

\sqrt{4} \times \sqrt{5}

2 \times \sqrt{5}

■We look for the largest square dividing

45

9

3^{2}

, and take it out of the root:

\sqrt{45}

\sqrt{9 \times 5}

\sqrt{9} \times \sqrt{5}

3 \times \sqrt{5}

2 \times 2 \times \sqrt{5}

- 2 \times \sqrt{5}

+ 3 \times 2 \times \sqrt{5}

- 2 \times 3 \times \sqrt{5}

ⓘ Multiplications are done before additions and subtractions:

2 \times 2

4

3 \times 2

6

2 \times 3

6

4 \times \sqrt{5}

- 2 \times \sqrt{5}

+ 6 \times \sqrt{5}

- 6 \times \sqrt{5}

ⓘ Like terms are grouped by adding their coefficients:

4 \times \sqrt{5}

- 2 \times \sqrt{5}

+ 6 \times \sqrt{5}

- 6 \times \sqrt{5}

2 \times \sqrt{5}

▶Simplified form:

2 \times \sqrt{5}

The numeric value of:

2 \times \sqrt{5}

is:

2 \times \approx 2.2361

▷

\approx 4.4721