Answer:
Method 1: -2√6 + √38 (approx. 1.26543)
Method 2: √2*(√19 - 2√3) (approx. 1.26543)
Explanation:
Method 1:
The answer format wasn't specified so here are both methods:
We can first think of - √24 as √24, and solve for the simplified version of the square root:
to simplify a square, factor out a perfect square from the radicand.
-Since we know that 4 times 6 equals 24, we can set 4 as our perfect square, with 2^2=4. With this in mind, the √24 turns into √2*2*6. When now a number with a square root is squared, the square root is removed.
For example, if we had √9, or √3^2, we can remove the √ and get 3 instead. The same applies to √(2)^2:
-√(2)^2 will now equal 2 since a square root squared will make the radical sign "disappear".
Our new equation is 2√6
With the negative sign in front of - √24, we multiple -1 * 2 to get:
-2√6
However, for the √38, a perfect square can not be factored out. Our new equation is:
-2√6 + √38
or approx. 1.26543
Method 2:
We can factor the whole expression - √24 + √38 to get a different simplified expression:
√2 can be factored out of the whole expression - √24 + √38
this makes - √24 + √38 become √2*(√19 - √12)
As mentioned in method one, while the √19 does not have a perfect square, the - √12 does, with 4, or 2^2 being applicable to factor out:
-√12
-√2^2 *√3
-2√3
So our new expression is:
√2*(√19 - 2√3)
or approx. 1.26543