## anonymous one year ago How do you solve the square root of the square root of 32 without a calculator

1. jim_thompson5910

this page may help http://www.homeschoolmath.net/teaching/square-root-algorithm.php let me know if it does or not

2. anonymous

I just need to know how to get rid of the double radical

3. jim_thompson5910

can you post the problem?

4. anonymous

Like how do I write that as a single radical expression

5. anonymous

101 a and b

6. jim_thompson5910

which problem number?

7. anonymous

@jim_thompson5910

8. jim_thompson5910

101a ?

9. anonymous

101 A and B

10. jim_thompson5910

ok

11. jim_thompson5910

|dw:1439767950197:dw|

12. jim_thompson5910

|dw:1439767977079:dw|

13. jim_thompson5910

|dw:1439768004175:dw|

14. jim_thompson5910

|dw:1439768026610:dw| making sense so far?

15. anonymous

Sorry what

16. anonymous

That's all I see

17. jim_thompson5910

oh, strange. Your browser isn't showing you the images I'm drawing

18. jim_thompson5910

You agree that $\LARGE \sqrt{32} = 32^{1/2}$ right?

19. anonymous

Can you screen shot them?

20. anonymous

Oh yes

21. jim_thompson5910

so that means $\LARGE \sqrt{\sqrt{32}} = \left(32^{1/2}\right)^{1/2}$

22. jim_thompson5910

Multiply the exponents and then convert back to radical form $\LARGE \sqrt{\sqrt{32}} = 32^{1/2*1/2}$ $\LARGE \sqrt{\sqrt{32}} = 32^{1/4}$ $\LARGE \sqrt{\sqrt{32}} = \sqrt[4]{32}$

23. anonymous

Oh okay!!! Oh my gosh yeah

24. jim_thompson5910

Optionally you can simplify this radical by doing this $\LARGE \sqrt{\sqrt{32}} = \sqrt[4]{32}$ $\LARGE \sqrt{\sqrt{32}} = \sqrt[4]{16*2}$ $\LARGE \sqrt{\sqrt{32}} = \sqrt[4]{16}*\sqrt[4]{2}$ $\LARGE \sqrt{\sqrt{32}} = 2*\sqrt[4]{2}$

25. anonymous

Oh my gosh!!! THANK YOU!!! God bless

26. jim_thompson5910

no problem