Simplifying radicals??

Question

ok can dome explain the tree prime method? 4 ex 120 simplifed is 2-/15. srry no sq root sign. but wouldnt it be 2-/30 ?? y would u divide it by 2? wat if u get decimals?

i need help/ explanations with

simplyfing 180

486

200

80

512 thx

Answer 1

~~~Sorry if some of these calculations are off; it's late at night! :/ Also, * means times.

180 = -/9*20 = 3 -/20 = 3 -/4*5 = 3*2 -/5 = 6 -/5

So 180 simplified would be six square root five.

486 = -/9*54 = 3 -/54 = 3 -/9*6 = 3*3 -/6 = 9 -/6

486 is equal to nine square root six.

200 = -/100*2 = 10 -/2

Two hundred is equal to ten square root two.

80 = -/16*5 = 4 -/5

Eighty is equal to four, square root five.

512 = -/16*32 = 4 -/32 = 4 -/16*2 = 4*4 -/2 = 16 -/2

Sixteen square root two is the answer.

And to answer your question, to simplify radicals you must first find a perfect square that goes into the whole number. I'll use your example, 120. So think of your perfect squares; 4, 9, 16, 25, and so on. We know four goes into one twenty, and that's a perfect square, so we divide 120 by four to get the number you have to multiply four by to get 120. That number is thirty. You put 4*30 under the square root sign, so right now we have -/4*30. Next, we "take" the perfect square out from under the radical, by taking the square root of that perfect square. We're left with 2 -/30, because 2*2 = 4. Since there are no more perfect squares that go into thirty, we are done! So yes, the answer should be 2 -/30, not 2 -/15.

So sorry if any of that confused you!

What do you mean biggest prime number?

You're very welcome, just make sure you pick me as the right answer ;-)