Question

Which value is equal to 4√20 - 3√45?
1) -√5
2) √5
3) 11√5
4) -11√5

Answer 1

The expression 4√20 - 3√45 is simplified to -√5 after breaking down the square roots into prime factors and combining like terms. Therefore, the correct answer is option 1) -√5.

Step-by-step explanation:

To solve 4√20 - 3√45, we need to simplify the square roots first. We can break down each square root into its prime factors:

• √20 = √(4×5) = √4×√5 = 2√5
• √45 = √(9×5) = √9×√5 = 3√5

Now we substitute these simplifications into the original expression:

4√20 - 3√45 = 4(2√5) - 3(3√5) = 8√5 - 9√5

Combining the like terms:

8√5 - 9√5 = (8 - 9)√5 = -1√5 = -√5

So the value of 4√20 - 3√45 is -√5, which corresponds to option 1).