I'm stuck on this one problem. The directions say:
Solve the following leaving the sq. rt. in it's simplest form:
sq.rt of 33+ sq.rt of 96 - sq.rt of 3 =
I think it can't be simplifed---am I correct? (the directions did say that some of the problems can't be simplified).
√33 + √96 - √3
= √33 + 4√6 - √3
that's about it.
To simplify the expression involving square roots, let's start by simplifying each square root individually.
√33 cannot be simplified because it does not have any perfect square factors. Therefore, we leave it as it is.
√96 can be simplified. To find the simplified form, we need to identify the perfect square factors of 96. The perfect square factors of 96 are 16 and 6. Since 6 is not a perfect square, we cannot use it. We can use 16, which is a perfect square equal to 4^2. Therefore, √96 can be written as √(16 × 6) = √16 × √6 = 4√6.
√3 cannot be simplified because it does not have any perfect square factors. So we leave it as √3.
Now, let's substitute these simplified square roots back into the original equation:
√33 + √96 - √3 = √33 + 4√6 - √3
Since there are no more simplifications we can make, this is the simplest form of the equation. Therefore, you were correct in thinking that it cannot be further simplified.