express 5�ã72 in simplest radical form
I did this:
�ã72=�ã36*�ã2=6�ã2
6*5=30
30�ã2
Is this right?
I guess maybe we are doing:
5 sqrt(72)
5 sqrt(36) sqrt(2)
30 sqrt(2)
Oh, it didn't come out right
The question was express (5)(sqrt)(72) in simplest radical form
I did:
sqrt(72)=sqrt(36)*sqrt(2)=(6)sqrt(2)
6*5=30
(30)sqrt(2)=answer
Am I on the right track?
Yes, that is fine.
Yes, your approach is correct. To express 5√72 in the simplest radical form, you can simplify the square root of 72 by factoring it into its prime factors:
√72 = √(2^3 * 3^2)
Next, you can separate the prime factors into two groups. Since the square root should be simplified as much as possible, one group will contain the factors with a power of 2 (2^3), and the other group will contain the factors with a power of 1 (3).
√72 = √(2^3) * √(3^2)
Now, simplify each square root separately:
√(2^3) = √8 = 2√2
√(3^2) = √9 = 3
Finally, multiply the simplified radical parts together:
5 * (2√2) * 3 = 30√2
So, the expression 5√72 in the simplest radical form is 30√2. Your answer is correct!