## anonymous 5 years ago In a paragraph, describe how to simplify each expression. 16 1/2 Square root 100

1. anonymous

????????? why don't u use the equation box to write yr question...

2. anonymous

In a paragraph, describe how to simplify each expression. 16 1/2 $\sqrt{100}$

3. anonymous

is the first one $16^{1/2}$ ???

4. anonymous

yes

5. anonymous

pls note that $x ^{1/2} = \sqrt{x}$

6. anonymous

why is that

7. anonymous

okay I will explain thru an example...

8. anonymous

ok awesome

9. anonymous

u know that $\sqrt{4}= 2$ also $(4)^{1/2} = (2^{2})^{1/2} = 2^{2*1/2} = 2^{1}=2$

10. anonymous

so we find that $\sqrt{4} = (4)^{1/2}$ because both give same result i.e. 2

11. anonymous

$({8}^2)$

12. anonymous

confused

13. anonymous

so we can solve the first one as $(16)^{1/2} = (4^{2})^{1/2} = 4^{2*1/2} = 4^{1}=4$

14. anonymous

what is confusing u???

15. anonymous

Oh because 4x4=16 right

16. anonymous

yes

17. anonymous

So $\sqrt{100}= 10$

18. anonymous

You might want to introduce and include rules of exponents and roots as part of your explanation.

19. anonymous

yes that is correct

20. anonymous

ok i understood the steps now

21. anonymous

ok i understood the steps now

22. anonymous

see square and root are opposite operations. so when they occur together, they cancel each other out.... we can show the working for root100 as follows : $\sqrt{100}=\sqrt{10^{2}}=10$ the square inside and root outside cancel each other out

23. anonymous

are u familiar with exponential laws???

24. anonymous

makes sense

25. anonymous

not really but i can try to find it in my book

26. anonymous

yes, u shud have all the laws in front of you and slowly try to learn them by heart....

27. anonymous

ok thank u

28. anonymous

u r welcome, just keep in mind... $\sqrt{x}=x ^{1/2}$ $\sqrt[3]{x}=x ^{1/3}$ $\sqrt[4]{x}=x ^{1/4}$ and so on....