Simplify the expression by rationalizing the denominator:?

Question

squared10/2

Answer 1

I agree with them it makes sense you want: square root of (10/2) {which most here would write someting like this: sqrt(10/2) } and for it to be simplified by rationalizing it must have an interim stage with a non-rational number in the denominator so, since the square root of a fraction equals the square root of the dividend divided by the square root of the divisor:

sqrt(10) / sqrt(2)

and to rationalize it, multiply by one in the form of sqrt(2) / sqrt(2):

{sqrt(10) * sqrt(2)} / {(sqrt(2) * sqrt(2)} so: {sqrt(10) * sqrt(2)} / 2 because a square root of a number multiplied by itself is the number (in this case 2).

Then simplify the top (you just did the "by rationalizing the denominator") by realizing 10 = 5 * 2 so you have the square root of 2 being multiplied by itself there as well so: 2 * sqrt(5) / 2 and it should be pretty obvious the 2's cancel so: sqrt(5) (the square root of 5) is the answer and this path rationalizes the denominator.

Answer 2

There doesn't seem to be a denominator to rationalize. Can you be more clear?

To represent the square root of 2, for instance, a good way to do it through here is to say sqrt(2).

I'm not entirely sure what you mean when you say "squared 10".

Answer 3

but the denominator is already rational
you mean 10/ sq.rt.2
=10rt2/2
=5rt2

Answer 4

100/4

Answer 5

I think you mean square root (not squared)
sqrt(10/2)
= sqrt(5)