Question

6) 3 √ 20-0,5 √80+2 √ 45.

Answer 1

$3 \sqrt{20} - 0.5 \sqrt{80} + 2 \sqrt{45} = 3 \sqrt{2 {}^{2} \times 5} - 0.5 \sqrt{ {4}^{2} \times 5} + 2 \sqrt{ {3}^{2} \times 5} = 3 \times 2 \sqrt{5} - 0.5 \times 4 \sqrt{5} + 2 \times 3 \sqrt{5} = 6 \sqrt{5} - 2 \sqrt{5} + 6 \sqrt{5} = (6 - 2 + 6) \sqrt{5} = 10 \sqrt{5}$

Answer 2

To simplify the expression 3√20 - 0.5√80 + 2√45, we can simplify each square root term individually and then perform the addition and subtraction.

Let's simplify each term:

1. √20: The square root of 20 can be simplified as follows: √20 = √(4 * 5) = √4 * √5 = 2√5

2. √80: The square root of 80 can be simplified as follows: √80 = √(16 * 5) = √16 * √5 = 4√5

3. √45: The square root of 45 can be simplified as follows: √45 = √(9 * 5) = √9 * √5 = 3√5

Now let's substitute the simplified terms back into the expression:

3√20 - 0.5√80 + 2√45 = 3(2√5) - 0.5(4√5) + 2(3√5)

Now we can simplify further:

= 6√5 - 2√5 + 6√5 = (6√5 + 6√5) - 2√5 = 12√5 - 2√5 = 10√5

Therefore, the simplified expression is 10√5.