Question

An expression is shown below:

square root of 50 plus square root of 2

Which statement is true about the expression?
It is irrational and equal to 2 multiplied by the square root of 13.
It is irrational and equal to 6 multiplied by the square root of 2.
It is rational and equal to 2.
It is rational and equal to 6. @Jhannybean

Answer 1

Well,how would you factor 50?

Answer 2

10*5

Answer 3

And 10?

Answer 4

so wat should i do now

Answer 5

How would you factor 10 first :P

Answer 6

2*5

Answer 7

Alright, so we have \[\sf \sqrt[2]{50} =\sqrt[\color{red}2]{ \color{red}{5 \cdot 5} \cdot 2 }\] you see that little 2 on top of the square root? It tells you how many of the same number can be pulled out of the square root.

Answer 8

So what would it simplify to?

Answer 9

uhh im not shore

Answer 10

under a square root, we can pull out pairs of 2 like-numbers. In this case we have 2 5's. When we pull them out it reduces it to just 1. So which numbers would we pull out?

Answer 11

5

Answer 12

Alright, so then we would have \[5\sqrt{2}\]

Answer 13

Now our problem states that \(5\sqrt{2}\) is added to \(\sqrt{2}\). \[5\sqrt{2} +\sqrt{2}\]Adding these together is like grouping like-terms together, all we have to do is add the coefficients infront of the radicals, and keep the bases. \[5\sqrt{2} +1\sqrt{2} = (5 +1)\sqrt{2}\]

Answer 14

So what do you get?

Answer 15

u r 2 smart can u dum this down a bit

Answer 16

What part do you understand up to so far? :o

Answer 17

factor

Answer 18

Hmm. Ok let's see.