Question

5√20+3√45−2√80−4√125

Answer 1

$5 \sqrt{20} + 3 \sqrt{45} - 2 \sqrt{80} - 4 \sqrt{125} = 5 \sqrt{4 \times 5} + 3 \sqrt{9 \times 5} - 2 \sqrt{16 \times 5} - 4 \sqrt{25 \times 5} = \\ \\ = 5 \times 2 \sqrt{5} + 3 \times 3 \sqrt{5} - 2 \times 4 \sqrt{5} - 4 \times 5 \sqrt{5} = 10 \sqrt{5} + 9 \sqrt{5} - 8 \sqrt{5} - 20 \sqrt{5} = - 9 \sqrt{5}$

Answer 2

To simplify the given expression, let's start by simplifying each of the square roots:

√20 = √(4 × 5) = 2√5 √45 = √(9 × 5) = 3√5 √80 = √(16 × 5) = 4√5 √125 = √(25 × 5) = 5√5

Now, substitute these values back into the expression:

5√20 + 3√45 - 2√80 - 4√125 = 5(2√5) + 3(3√5) - 2(4√5) - 4(5√5)

= 10√5 + 9√5 - 8√5 - 20√5

= (10 + 9 - 8 - 20)√5

= -9√5

So, the simplified form of the expression 5√20 + 3√45 - 2√80 - 4√125 is -9√5.