To simplify the expression 7√20z + √45z, we can start by simplifying the square roots.
First, let's simplify √20 and √45.
√20 can be simplified as follows:
√20 = √(4 * 5) = 2√5
√45 can be simplified as follows:
√45 = √(9 * 5) = 3√5
Now, let's substitute these simplified square roots back into the original expression:
7√20z + √45z = 7(2√5z) + 3√5z
Next, we can simplify the expression further by combining like terms. In this case, the like terms are the terms with the same radical (√5z).
7(2√5z) + 3√5z = 14√5z + 3√5z
Combining these terms, we get:
14√5z + 3√5z = (14 + 3)√5z = 17√5z
So, the simplified form of the expression 7√20z + √45z is 17√5z.
I hope this explanation helps! Let me know if you have any other questions.