# Adding and Subtracting Radicals

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• Feb 12th 2011, 07:53 AM
chandler
Adding and Subtracting Radicals
How would you simplify and do these problems?

(square root of) 2/5 + (square root of) 1/2

8 - (square root of) 5/7

I understand the concept... I just always get these wrong for some reason, so please be detailed so I can understand! Thanks!
• Feb 12th 2011, 08:01 AM
Plato
Quote:

Originally Posted by chandler
How would you simplify and do these problems?

(square root of) 2/5 + (square root of) 1/2

8 - (square root of) 5/7

I understand the concept... I just always get these wrong for some reason, so please be detailed so I can understand! Thanks!

Are there two separate questions there?

Is the first one $\sqrt {\dfrac{2}{5}} + \sqrt {\dfrac{1}{2}}~?$
• Feb 12th 2011, 08:23 AM
chandler
Yes, two seperate
Yes, these are two different equations.

Also... How do you make the square root symbol?
• Feb 12th 2011, 08:26 AM
Prove It
Quote:

Originally Posted by chandler
How would you simplify and do these problems?

(square root of) 2/5 + (square root of) 1/2

8 - (square root of) 5/7

I understand the concept... I just always get these wrong for some reason, so please be detailed so I can understand! Thanks!

$\displaystyle \sqrt{\frac{2}{5}} + \sqrt{\frac{1}{2}} = \sqrt{\frac{4}{10}} + \sqrt{\frac{5}{10}}$

$\displaystyle = \frac{\sqrt{4}}{\sqrt{10}} + \frac{\sqrt{5}}{\sqrt{10}}$

$\displaystyle = \frac{\sqrt{4} + \sqrt{5}}{\sqrt{10}}$

$\displaystyle = \frac{2 + \sqrt{5}}{\sqrt{10}}$

$\displaystyle = \frac{\sqrt{10}(2 + \sqrt{5})}{10}$

$\displaystyle = \frac{2\sqrt{10} + \sqrt{50}}{10}$

$\displaystyle = \frac{2\sqrt{10} + \sqrt{25}\sqrt{2}}{10}$

$\displaystyle = \frac{2\sqrt{10} + 5\sqrt{2}}{10}$.
• Feb 12th 2011, 08:38 AM
Plato
Quote:

Originally Posted by chandler
How do you make the square root symbol?

$$\sqrt {\dfrac{2}{5}} + \sqrt {\dfrac{1}{2}}$$ gives $\sqrt {\dfrac{2}{5}} + \sqrt {\dfrac{1}{2}}$
• Feb 12th 2011, 09:08 AM
chandler
Thanks guys!
One more thing...

Please do this one too: $\sqrt {\dfrac{1}{2}} + \sqrt {\dfrac{1}{2}}$ =
• Feb 12th 2011, 09:12 AM
Plato
Quote:

Originally Posted by chandler
One more thing...

Please do this one too: $\sqrt {\dfrac{1}{2}} + \sqrt {\dfrac{1}{2}}$ =

$\sqrt {\dfrac{1}{2}}={\dfrac{\sqrt2}{2}}$