okay I know you said you leave the square root alone but I don't think so on this one (see pic) @johnweldon1993

Question

johnweldon1993 · Answer

lol okay show me :)

anonymous · Answer

$$\sqrt{8}+\sqrt{50}$$

johnweldon1993 · Answer

Ahh yes...well this is another case :)

Well lets see....what are all the numbers that multiply to make 8?

1, 2, 4, and 8 right? Lets ask ourselves...which of these is a perfect square? hmm well 4 is 2² so lets use that

$$\sqrt{8} = \sqrt{2}\sqrt{4}$$

See what I did there?

And now we can simplify that because we know √4 is 2

$$\sqrt{8} = 2\sqrt{2}$$

We can do this to the other one as well...50...what 2 numbers *making 1 a perfect square* multiply to make 50?

johnweldon1993 · Answer

I hope that made sense??

Here just let me continue and you can ask if theres a part thats confusing

$$\sqrt{8} + \sqrt{50}$$

can become

$$\sqrt{2}\sqrt{4} + \sqrt{2}\sqrt{25}$$

This is because we know that √2 times √4 = √8.....and √2 times √25 = √50

Now this is helpful for us...because we know that 4 is a perfect square of 2.....and we know that 25 is a perfect square of 5     *2² = 4 and 5² = 25*

so now when we simplify this...we have

$$2\sqrt{2} + 5\sqrt{2}$$

Now we have add them like the questions before...

anonymous · Answer

25 is one and.........(thinking)......uhmmm.......i cant think of another one:P sorry

johnweldon1993 · Answer

Ahh yeah see that is what I was going for! lol....25 times 2 = 50....and we only need 1 number to be a perfect square...which is the one that we needed here 25 = 5².....good job...now refer to the above post :)

anonymous · Answer

$$7\sqrt{2}$$  would this be my total answer?? @johnweldon1993

johnweldon1993 · Answer

That would be correct! :)