Which of the following is equivalent to the expression below sqrt 8 - sqrt 72 + sqrt 50 A. sqrt 2
B. 3 sqrt 2
C. 13 sqrt 2
D. 7 sqrt 2

Step-by-step explanation:

These cannot combine the way they are. The rule for adding and subtracting radicals is really picky. Not only does the index have to be the same (the little number that is sitting outside in the bend of the radical {ours is a 2, which isn't usually there, but is instead understood to be a square root}), but the radicand, the expression under the square root (or cubed root, or fourth root, etc) has to the same as well. All of our radicals are square roots, so that's good, but the radicands are all different. The first one is an 8, the next one is a 72, and the last one is a 50. BUT if we can rewrite them by simplifying them and then the radicands are the same, we're in good shape.

Simplify by taking the prime factorization of each of those numbers.

8: 4*2 and 4 is a perfect square, so we'll stop there

72: 36*2 and 36 is a perfect square, so we'll stop there

50: 25*2 and 25 is a perfect square, so we'll stop there.

Now, rewrite each one of them in terms of their prime factorization:

and then pull out each perfect square as its root:

and now all the radicands are the same, so we can add them to get

 or simply  

Step-by-step explanation:

sqrt 8 = sqrt (2 * 2 *2 ) =

sqrt 72 = sqrt (2 * 2 *2 * 3 * 3 ) =

sqrt 50= sqrt (2 * 5 *5 ) =

the mistake in the pattern is that :

b. the decimal point was moved one too many place values each time

the correct pattern could be made by :

b. moving the decimal point to the right the same numbers of place values as the exponents

step-by-step explanation:

you can add the two numbers and divide the result by 2. or you can find the gap between the two numbers and add half of this to the smaller number.