SIMPLIFY THE RADICAL!!

Thanks Max, I am told your interpretation is correct :)

 

Hi Lisa,

How do you simplify (1+( sqrt 2/2) / (sqrt 2/2)

so you question is

 

How do you simplify (1+( sqrt 2/2)) / (sqrt 2/2)

or better still

How do you simplify(1+( (sqrt 2)/2)) / ((sqrt 2)/2)

 

This is how I would do it

 

\(\frac{1+\frac{\sqrt 2}{2}}{\frac{\sqrt 2}{2}}\\ =(1+\frac{\sqrt 2}{2})\div{\frac{\sqrt 2}{2}}\\ =(1+\frac{\sqrt 2}{2})\times{\frac{2}{\sqrt 2}}\\ \qquad \text{I want a rational denominator so if I multiply the bottom by sqrt2 }\\ \qquad \text{but what I do to the bottom I must do to the top as well because I am really multiplying by1}\\ =(1+\frac{\sqrt 2}{2})\times{\frac{2}{\sqrt 2}}\times\frac{\sqrt2}{\sqrt2}\\ =(1+\frac{\sqrt 2}{2})\times{\frac{2\sqrt2}{2}}\\ =(1+\frac{\sqrt 2}{2})\times\sqrt2\\ =\sqrt2(1+\frac{\sqrt 2}{2})\\ =\sqrt2+\frac{2}{2}\\ =\sqrt2+1\\\)

 

Now, if you still do not quite understand Lisa, make sure you say so :)

your brackets are not balanced Lisa ....

perhaps you mean

 

(1+ sqrt( 2/2)) / (sqrt (2/2))     ??

 

or

(1+(( sqrt 2)/2)) / ((sqrt 2)/2)   ??

 

or

 

something else???

\(\text{Q:Simplify }\dfrac{1+\frac{\sqrt2}{2}}{\frac{\sqrt2}{2}}\)

\(\quad\dfrac{1+\frac{\sqrt2}{2}}{\frac{\sqrt2}{2}}\\ =\dfrac{1}{\frac{\sqrt2}{2}}+\dfrac{\frac{\sqrt2}{2}}{\frac{\sqrt2}{2}}\\ =2\div \sqrt2 + 1\qquad\color{olive}\boxed{\color{red}2=(\sqrt2)^2}\\ = \sqrt2 + 1\)

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