How do you simplify # sqrt (0.5)#?

1 Answer

Answer:

#sqrt2/2#

Explanation:

The difficult part here is dealing with a decimal inside the root sign. So let's change that to a fraction and see if it's easier to deal with:

#sqrt.5=sqrt(1/2)#

This is good - there is now no decimal inside the root. But now we have to deal with a root in the denominator of our fraction. So let's get rid of it through a creative use of multiplying by 1:

#sqrt(1/2)=sqrt1/sqrt2=(1/sqrt2)(1)=(1/sqrt2)(sqrt2/sqrt2)=sqrt2/2#