3sqrt(7)-3sqrt(64)+7sqrt(112)
To simplify the expression 3√7 - 3√64 + 7√112, we can start by simplifying the square roots.
First, let's simplify √64. The square root of 64 is 8, because 8 multiplied by itself gives 64.
Next, let's simplify √112. Since 112 is not a perfect square, we can simplify it by finding the largest perfect square that is a factor of 112. The largest perfect square that is a factor of 112 is 16, because 16 multiplied by 7 gives 112.
Therefore, √112 can be written as 4√7, because √16 is 4.
Our expression now becomes: 3√7 - 3(8) + 7(4√7).
Simplifying further, we have: 3√7 - 24 + 28√7.
Now, we can combine like terms. We have two terms with √7: 3√7 and 28√7.
Adding these terms together, we get: 31√7.
Our expression now becomes: 31√7 - 24.
Therefore, the simplified expression of 3√7 - 3√64 + 7√112 is 31√7 - 24.