Question

MEDAL AWARDED ON SPOT

Answer 1

What do you need hun? (:

Answer 2

Okay. Just give me a second to work it out!

Answer 3

Okay, so I am going to explain it okay? Here it is:

Answer 4

Okay, so we are trying to simplify 2√20 + 8√45 + √80

First, we simplify 2√0.

If you use a guess and check method, you see that -12 = 1 and 12 = 1.
Since 1 < 0 < 1 the next logical step would be checking 02.

02 = 0 x 0
02 = 0 <--- We match our original number!!! :D
Multiplying by our outside constant, we get 2 x 0 = 0
Therefore, 2√0 = ±0

Now we simplify 8√0.

If you use a guess and check method, you see that -12 = 1 and 12 = 1.
Since 1 < 0 < 1 the next step would be checking 02.

02 = 0 x 0
02 = 0 <--- We match our original number (AGAIN!)!!!
Multiplying by our outside constant, we get 8 x 0 = 0
Therefore, 8√0 = ±0

the next step is to simplify √80.

Checking square roots, we see that 82 = 64 and 92 = 81.
Since our answer is not an integer, we will try simplify it into the product of an integer and a radical.

We do this by listing each product combo of 80 checking for integer square root values below:
√80 = √1√80
√80 = √2√40
√80 = √4√20
√80 = √5√16
√80 = √8√10
Like that^^^^^

From that list, the highest factor that has an integer square root is 16.
Therefore, we use the product combo √80 = √16√5
Evaluating square roots, we see that √16 = 4

Simplifying our product of radicals, we get our answer:
√80 = 4√5

Simplifying the original expression, we get:
Group Constants → 0
Group √5 terms → 4√5 = 4√5

Build our final simplified answer:
0 + 4√5

Understand?