Question

-2√80+√320-4√20+√45= 4√90-√10-3√160-5√40=

Answer 1

-2√16*5+√16*20-4√20+√9*5=-8√5+4√20-4√20+3√5= -5√5

4√9*10-√10-3√16*10-5√4*10 = 12√10-√10-12√10-10√10= -11√10

Answer 2

To simplify the expressions, let's start by simplifying the square roots of the numbers:

1. √80 = √(16 * 5) = √16 * √5 = 4√5
2. √320 = √(64 * 5) = √64 * √5 = 8√5
3. √20 = √(4 * 5) = √4 * √5 = 2√5
4. √45 = √(9 * 5) = √9 * √5 = 3√5
5. √90 = √(9 * 10) = √9 * √10 = 3√10
6. √10 remains the same.
7. √160 = √(16 * 10) = √16 * √10 = 4√10
8. √40 = √(4 * 10) = √4 * √10 = 2√10

Now, let's rewrite the expressions with the simplified square roots:

-2√80 + √320 - 4√20 + √45 = -2(4√5) + 8√5 - 4(2√5) + 3√5 = -8√5 + 8√5 - 8√5 + 3√5 = -8√5 + 8√5 - 8√5 + 3√5 = -5√5

4√90 - √10 - 3√160 - 5√40 = 4(3√10) - √10 - 3(4√10) - 5(2√10) = 12√10 - √10 - 12√10 - 10√10 = 12√10 - 12√10 - √10 - 10√10 = 0 - 11√10 = -11√10

So the simplified expressions are: -2√80 + √320 - 4√20 + √45 = -5√5 4√90 - √10 - 3√160 - 5√40 = -11√10