Question #95e73

2 Answers
Mar 9, 2017

sqrt(2)/2

Explanation:

sqrt((1/2)^2+(1/2)^2)

First find out what (1/2)^2 is:

(1/2)^2 = 1/4

So, we now know that the expression is now sqrt(2/4) which is the same as sqrt(1/2).

Then, we rationalize the denominator as we cannot have a root as
the denominator:

sqrt(1) = 1, so the expression is now 1 /sqrt(2)

Multiply both the numerator and the denominator by sqrt(2)

Denominator = sqrt(2) * sqrt(2) = 2

Numerator = 1 * sqrt(2) = sqrt(2 )

Hence,

= sqrt(2)/2

Mar 9, 2017

The expression is equivalent to sqrt(2)/2.

Explanation:

The square of 1/2 is 1/4 because (1/2)(1/2) = 1/(2*2) = 1/4.

Therefore,

sqrt(1/4 + 1/4)

sqrt(2/4)

sqrt(1/2)

We can separate the radicals.

sqrt(1)/sqrt(2)

1/sqrt(2)

I would recommend you rationalize the denominators.

1/sqrt(2) * sqrt(2)/sqrt(2)

sqrt(2)/2

Hopefully this helps!