Can someone help me with these...plz
Simplify
2radical (12) + 4 radical (27)
if i simplify radical (12) i get 2radical (3) then if i simplify radical (27) i get 3radical (3). so now i don't know if i'm doing this correctly or how to set it up...
2 sqrt 12 + 4 sqrt 27
4 sqrt 3 + 12 sqrt 3
16 sqrt 3
how did you do this can you explain it to me please. I want to really understand this type of math...But i am just not seeing it...Can you explain to me the steps that you did please...
Sure! I'd be happy to explain the steps to simplify the expression 2√12 + 4√27.
To simplify square roots, we want to simplify the numbers inside the square roots as much as possible before combining like terms. Here's how you can do it step by step:
Step 1: Simplify the numbers inside the square roots.
Start by simplifying √12 and √27.
To simplify √12, you need to find the largest perfect square that divides evenly into 12. In this case, it is 4. So we can rewrite it as √(4 × 3). Since the square root of 4 is 2, we get 2√3.
Similarly, to simplify √27, you need to find the largest perfect square that divides evenly into 27. In this case, it is 9. So we can rewrite it as √(9 × 3). Since the square root of 9 is 3, we get 3√3.
Step 2: Combine like terms.
Now that we have simplified √12 and √27, we can combine the like terms.
The expression 2√12 + 4√27 becomes 2(2√3) + 4(3√3).
Step 3: Simplify further.
Multiply the coefficients (numbers in front of the square roots) with the simplified square roots.
2(2√3) means 2 multiplied by 2, which gives 4√3.
4(3√3) means 4 multiplied by 3, which gives 12√3.
Step 4: Combine like terms (if possible).
Finally, combine the like terms 4√3 and 12√3 by adding their coefficients, which are 4 and 12.
4√3 + 12√3 equals 16√3.
So the simplified expression is 16√3.
I hope this explanation helps you understand the steps involved in simplifying square roots!