Ugh...radicals...someone, please?

Question

Can someone PLEASE explain to me how to do radical divided by radical problems...such as this one: radical 28 divided by radical 7??? Please, I really do not understand it...in class, I thought it was four, but now getting home and reworking it a different way, I keep getting two...

Answer 1

Your second answer is right. Here's the work:

√28 / √7 = √(4*7) / √7 = (2√7)/√7 = 2

Answer 2

You mean the square root of 28 divided by the square root of 7.

V`28 / V`7

First: express "28" in lowest terms...

V`(4*7) / V`7

V`(2*2*7) / V`7

(2 V`7) / V`7

Sec: cancel "like" terms..

= 2

Answer 3

multiply top and bottom by square root of 7 to get square root times square root of 28 divided by square root of 7 squared. when two radicals are multiplied by each other, you just multiply the numbers under the roots, so 7*28, or 196. square root of that is 14. on the bottom, square root of 7^2 is 7, and 14/7 is two, so you did it right at home.

Answer 4

sqrt(28)/sqrt(7) = sqrt (28/7) = sqrt(4) = 2

In general, you can divide two radicals by dividing both numbers inside of one radical (just like if you want to multiply two radicals, you can multiple the two numbers inside the same radical)

that is sqrt(a)/sqrt(b) = sqrt(a/b) and sqrt(a)*sqrt(b)=sqrt(a*b)

but you cannot do addition and subtraction of radicals this way

sqrt(a) + sqrt(b) does not = sqrt(a+b)