Find the answer for - √24 + √38 =

Method 1:  -2√6 + √38 (approx. 1.26543)

Method 2: √2*(√19 - 2√3) (approx. 1.26543)

Step-by-step 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

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