Instead of doing all that work to simplify the mixed radical , can I just change the mixed radical into an entire radical?

Ex: 2* square root 18 into square root of 72

Yes, but if the instructions say to simplify then you can't do that.

Oh man.... I don't understand how to simplify though... Can u please help me with These questions :

2 * square root 18
5* square root 48
3* square root 54

Look for perfect squares that divide the radicand.

√18 = √9*√2 = 3√2
So, 2√18 = 2*3√2 = 6√2

5√48 = 5√(16*3) = 5√16*√3 = 5*4√3 = 20√3

3√54 = 3√(9*6) = 3√9*√6 = 3*3√6 = 9√6

Alright now I understand ! Thank u sooooo much:)

Yes, you can simplify a mixed radical by changing it into an entire radical. To do this, follow these steps:

Step 1: Write the integer outside the radical sign as a separate factor.
In your example, you have 2 * √18.

Step 2: Simplify the number inside the radical sign.
To simplify the number inside the radical sign (√18), you can find the largest perfect square that is a factor of 18. In this case, it is 9, since 9 * 2 = 18.

Step 3: Rewrite the entire radical.
You can rewrite the entire radical by multiplying the factor outside the radical by the simplified number inside the radical. In this case, it would be 2 * √(9 * 2) = 2 * √9 * √2.

Step 4: Simplify the remaining radical.
The square root of 9 (√9) is equal to 3. So, the simplified entire radical expression would be 2 * 3 * √2 = 6√2.

Therefore, 2 * √18 can be simplified to 6√2.