When adding radicals, do you add two radicands together even if they're different?
How would you answer this equation in radical simplest form?
3 rad 12 + 3 rad 12 + 5 rad 8 +5 rad 8
I got 6 rad 12 + 25 rad 8
Is this right? Sorry if my questions are confusing, this is hard to explain.
3√12 + 3√12 + 5√8 + 5√8
= 6√12 + 10√8
but √12 = √4√3 = 2√3
and √8 = √4√2 = 2√2
so 6√12 + 10√8
= 6(2√3) + 10(2√2)
= 12√3 + 20√2
(We can only add/subtract "like" radicals, but we can multiply/divide them in this way ...
e.g. √5x√7 = √35 , √60 ÷ √2 = √30 )
Thanks, now I remember the teacher quickly rushing through that in class. ;)
Calamity , if mathematics should ever be rushed ....
No problem! I can help clarify. When adding radicals, you can only combine like terms, which means the radicands (the numbers inside the radical symbol) must be the same. So, let's break down your expression step by step to simplify it.
We start with: 3√12 + 3√12 + 5√8 + 5√8
First, let's simplify the radicands:
√12 = √(4 × 3) = √4 × √3 = 2√3
√8 = √(4 × 2) = √4 × √2 = 2√2
Now we substitute the simplified radicands back into the equation:
3(2√3) + 3(2√3) + 5(2√2) + 5(2√2)
Next, we distribute the coefficients:
6√3 + 6√3 + 10√2 + 10√2
Combining like terms, we have:
(6√3 + 6√3) + (10√2 + 10√2) = 12√3 + 20√2
So, the simplified radical form of the equation is 12√3 + 20√2. Therefore, your answer of 6√12 + 25√8 is incorrect.
Remember to simplify the radicands before combining like terms. I hope this explanation helps! Let me know if you have any further questions.