## TeemoTheTerific 2 years ago Simplify (2^1/2 - 2^-1/2)^2 ill write it neater. Please help

1. TeemoTheTerific

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2. TeemoTheTerific

i know formula a^2 - 2ab + b^2

3. TeemoTheTerific

i dont get it :P

4. TeemoTheTerific

|dw:1359872887253:dw|btw original question is

5. TeemoTheTerific

thats original quesiton

6. hartnn

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7. TeemoTheTerific

yes your right now hartnn :)

8. hartnn

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9. hartnn

can you simplify that now ?

10. TeemoTheTerific

11. TeemoTheTerific

is there a way to do this question using indices laws?

12. TeemoTheTerific

cause my teacher prefers that :P

13. hartnn

yes, 5 is correct.

14. hartnn

i have used law od indices $$2^{1/2}.2^{1/2}= 2^{1/2+1/2}=2^1=2$$

15. hartnn

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16. hartnn

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17. hartnn

got that^ ?

18. TeemoTheTerific

yes thank you so much

19. hartnn

welcome ^_^

20. whpalmer4

$(2^{1/2} - 2^{-1/2})^2 = (2^{1/2}-2^{-1/2})(2^{1/2}-2^{-1/2})=$$2^{1/2}*2^{1/2}-2^{-1/2}2^{1/2} - 2^{-1/2}2^{1/2} + 2^{-1/2}2^{-1/2} =$$2^1-2^0-2^0+2^{-1} = 2 - 1 - 1 + \frac{1}{2} = \frac{1}{2}$

21. whpalmer4

Maybe easier to write $$a = 2^{1/2}$$ and $$b = a^{-1/2}$$ then $(a-b)^2 = a^2 - 2ab + b^2 = (2^{1/2})^{1/2} - 2*2^{1/2}*2^{-1/2} + (2^{-1/2})^2 =$$2^1 - 2*2^0 + 2^{-1} = 2^{-1} = \frac{1}{2}$ and use some different properties :-)