Express in simplest radical form
- square root 6 + 9 square root 24
To simplify the expression, we start by simplifying each square root separately.
The square root of 6 cannot be simplified any further.
The square root of 24 can be simplified by factoring out the largest perfect square. The largest perfect square that divides 24 is 4, which is equal to 2^2.
So, 24 can be written as 4 * 6.
Taking the square root of 4 gives us 2.
Now we can substitute these simplified square roots back into the original expression:
√6 + 9 * √24 = √6 + 9 * √(4 * 6)
Next, we can use the distributive property to simplify the expression further:
= √6 + 9 * √4 * √6
= √6 + 9 * 2 * √6
= √6 + 18 * √6
= (1 + 18) * √6
= 19√6
Therefore, the expression √6 + 9√24 can be simplified to 19√6 in its simplest radical form.