square roots!!! Help please

[Lisa L from MI]

DD-5th is doing her math. She needs to find the square root of numbers WITHOUT a calculator!! I am at a loss!! One is 729 and another is 225


Thanks for your help

 

[Steve H.]

Best way to go about it is trial and error.

For example, take 729: I know that 30 x 30 = 900, so I would guess maybe it's 26 squared. Multiply 26 x 26 and get 676, so I know it's higher than that. So, I try 27 and find that 27 x 27 = 729. Now, if it's not an evenly squared number, it's obviously a little trickier.

 

[Lisa L from MI]

thanks...that does make sense....I reread her directions on her homework and it doesn't say NOT to use a calculator...just not to use the square root key....so I guess she could use the "X" key to do the trial and error


Thanks again...

 

[Steve H.]

Nah -- I say make her do the multiplication on paper (or in her head, but that might be mean ).

 

[Toby'sFriend]

At the fifth grade level this is what I would suggest in order to make a good guess.

Keep it mind what the ending number is for each number 1 - 9 when it is multiplied by itself

1 * 1 = 1
2 * 2 = 2
3 * 3 = 9
4 * 4 = 16 -- so a 6
5 * 5 = 25 -- so a 5
6 * 6 = 36 -- so a 6
7 * 7 = 49 -- so a 9
8 * 8 = 64 -- so a 4
9 * 9 = 81 -- so a 1


for 729 she needs a number that ends in 9, so the number will be something that ends in a 7. My guess would be 27. At that point she just needs to get her pencil and paper and check. I just checked, I was right. She might have needed to start with 17, and then move to 27.

I hope that makes sense.

 

[alabamaalan]

Originally posted by Steve H.
Nah -- I say make her do the multiplication on paper (or in her head, but that might be mean ).

Nah, tell her to do the multiplication on paper using only Roman numerals. Now THAT'S mean!

 

[Towncrier]

There is a paper and pencil method for finding square roots. It looks a bit like long division. I can't quite remember how to do it, but I do remember being fascinated by the method when I was in school and that I got very good at determining square roots.

If she's allowed to use the internet, she could just go to Google and type "square root(255)" in the search field and it will give her the answer.

 

[WebmasterMaryJo]

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sheesh - edited for my real comment

Toby's Friend - I like that shortcut - thanks. I'll pass that along to my kids

 

[Pin Wizard]

Thanks, Toby! I copied that into WordPerfect for MY use! LOL!

 

[Cindy B]

I did this in my math class.... last semsester


Does she know divisibility rules?

She can add the numbers together and see if they are divisble by a certain number... and if they are divisible, she should be able to find out square roots.

I think one is an irrantional number so it may not be a perfect square root (but I may be wrong there!)

Does she know rational/irrational numbers?

 

[Breezy_Carol]

Towncrier, I think you are about my age. My dad was an engineer and could do a square root on paper. I wish I could remember how he showed me.

Then of course, there is always the slide rule.

 

[Lisa L from MI]

Toby'sfriend.....thats really interesting. I will print that out for her.

Not sure if she knows about rational/irrational numbers. Heck....I don't think I even do!!! And to think I was practically a straight A student!!.......many many moons ago!

 

[Steve H.]

Originally posted by Toby'sFriend
At the fifth grade level this is what I would suggest in order to make a good guess.

Keep it mind what the ending number is for each number 1 - 9 when it is multiplied by itself

1 * 1 = 1
2 * 2 = 2
3 * 3 = 9
4 * 4 = 16 -- so a 6
5 * 5 = 25 -- so a 5
6 * 6 = 36 -- so a 6
7 * 7 = 49 -- so a 9
8 * 8 = 64 -- so a 4
9 * 9 = 81 -- so a 1


for 729 she needs a number that ends in 9, so the number will be something that ends in a 7. My guess would be 27. At that point she just needs to get her pencil and paper and check. I just checked, I was right. She might have needed to start with 17, and then move to 27.

I hope that makes sense.

Couldn't it also have been a number ending in 3 as well? I like the technique, though, it does narrow down the guesses.

 

[damo]

There are no numbers that are perfect squares that have the last digit 2 or 3 or 7 or 8. (i.e. you can't take the exact square root).

 

[Towncrier]

Here is a link to a site that explains the "algorism" method of computing a square root. It's not as hard as it first appears.

http://www.du.edu/~jcalvert/math/sqrt.htm

 

[cgcw]

Oh my!! I will print this out for safe keeping. Only 2 years until DS8 is in 5th grade. Something to definately look forward to. I can't wait to help with this type of homework. I knew there was a reason I got out of computer programming.

 

[Pin Wizard]

Originally posted by cgcw
I knew there was a reason I got out of computer programming.

LOL! Isn't that the truth? I'd love to do something in the science field, but I'm not so sure I'd make it through all the courses to get there!