Simplifying Radicals help please again for the 3rd time, lol?

[lance]

The problem is 28 divided by the square root of 8. Please show work and explain, Thank You!

[BeeLiz19]

28 / ?8

always simplify radicals

?8

separate into factors, the left factor will be a perfect square that you will reduce:

?8 = ?4 x ?2

= 2 x ?2

SO our question is more like



28/2 x 28/?2

14/1 x 28/?2

392/?2

don't think you can simplify this further.

[iMaths]

28 / ?8

?8 can be expressed as a mixed radical, as follows:

?8 = ?4 * ?2
? ?8 = 2?2

28 / ?8 becomes 28 / (2?2)

Divide by the GCF, 2 to obtain 14 / ?2.

Next, rationalize the denominator by multiplying the faction by ?2 / ?2:

14?2 / 2

Simplify to obtain 7?2

[Josquine]

actually, you need to rationalize it first.

rationalize means multiplying the same number to numerator and denominator such that denominator should contain no radicals.

To do this, think of a number that if we multiply to ?8 will give us a perfect root number. Well in this case, we will multiply it to ?8.
Therefore, we get the new problem of 28(?8)/8.

We can simplify and or cancel 28 to 8 since the operation is multiplication.
We get, 7?8/2. This is now our final answer