Easy math question? radicals? Please help?

Question

I need help simplifying this radical:

So the problem is radical 800. I seperated it into 10 and 80. My answer was 2 radical 5 times 80.

But the answer in my book is 20 radical 2.
How did they get this?

Thanks.

Answer 1

Because 20*20=400. When you seperated it you probably meant 10 outside and 80 in the square, but to take something outside you have to take the square root. You could have taken the full 10 out, but the square of that is 100. you would still have "8" in there, but you can still factor that into 4 and 2, and take another 2 out (the 4 inside the radical). In this way the 2 and 10 are out, which when multiplied is 20 and the last 2 is still inside. 20 Sqof(2)

Answer 2

You split it up into (√10) (√80):



= (√10) (√16) (√5) ------> [Split up √80.]

= 4 (√50) ------------------> [√16 = 4, multiply √10 and √5 together.]

= 4 * 5√2 ------------------> [√50 = (√25) (√2) = 5√2]

= 20√2 ---------------------> [4*5 = 20]



Did you mean "2 radical 5 times 80" (160√5) or "2 times the radical of the quantity of 5 times 80" (2√400)? Either way I'm sorry, but I have no idea how you got your answer. Both √80 and √10 do not = 2√5.

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An easier way is to break it up like this:

√800

= (√100)(√8) --------> [√8 = (√4) (√2) = 2√2]

= (10)(2√2)

= 20√2



Because you know that 100 is a perfect square and that it is one of 800's biggest factors.

Answer 3

Ur close to that answer but u forgot something. u gave 5*80 radical 2 or 400(2)^1/2. (x radical equals x^1/2 "power of half" ) when u solve this u get a larger number. u would get first 400 * 400 = 160,000. then multiply this by 2 would give us

radical 320,000.

the second answer(the book). said 20 radical 2 or 20*(2)^1/2

when solving, multiply 20 by its self first. and u would get 400. then multiply 400 by 2. your would get 800. then put it in a radical. which gives us the first form.