My Math Forum Square Roots

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 November 6th, 2009, 07:34 PM #1 Newbie   Joined: Nov 2009 Posts: 3 Thanks: 0 Square Roots Hi, I'm not sure if this is the right place to post this. I'm doing grade 8 math and I'm learning square roots. What I'm learning right now is finding the square root of a number without a calculator. I understand how to find the square root of 5, 16, 3, 31 etc. The problem I'm having is finding the square of a decimal like 0.8, 0.08, 0.5, etc. What I want to know is how to estimate the value of the square root of 0.8, 0.08, 0.5, etc. What would the formula be so I can apply it to finding the squares of other decimals like these ones. Please help Thank You
 November 6th, 2009, 07:40 PM #2 Senior Member   Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3 Re: Square Roots The square root of 0.8 is equal to one tenth of the square root of 80. Multiply by 100. (And again, if necessary.) Find square root. Divide by 10. (Same number of times you multiplied by 100.)
 November 6th, 2009, 07:59 PM #3 Newbie   Joined: Nov 2009 Posts: 3 Thanks: 0 Re: Square Roots Thank you aswoods for replying. I'm sorry, maybe I've been at this too long, but I'm still not understanding it.
 November 6th, 2009, 08:18 PM #4 Senior Member   Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3 Re: Square Roots You said you knew how to estimate square roots of whole numbers, right? $\sqrt{0.8}= \sqrt{\frac8{10}} = \frac{\sqrt8}{\sqrt{10}} = \frac{\sqrt8}{\sqrt{10}}\times\frac{\sqrt{10}}{\sq rt{10}} =\frac{\sqrt{80}}{\sqrt{100}} = \frac{\sqrt{80}}{10}$ So you can estimate the square root of 80, then divide your estimate by 10. 80 is just below 81 ( = 9² ), so its square root will be just below 9. Therefore the square root of 0.8 will be just below 0.9.
 November 6th, 2009, 08:24 PM #5 Senior Member   Joined: Feb 2009 From: Adelaide, Australia Posts: 1,519 Thanks: 3 Re: Square Roots Problem 1: Estimate square root of 0.08 0.08 Multiply by 100 8 Estimate square root It's just below 9 ( = 3²), so 3 Divide by 10 0.3 (Correct value: 0.28284...) Problem 2: Estimate square root of 0.5 0.5 Multiply by 100 50 Estimate square root Just above 49 ( = 7²), so 7 Divide by 10 0.7 (Correct value: 0.7071...)
November 7th, 2009, 05:39 AM   #6
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Quote:
 Originally Posted by micheal2345 I understand how to find the square root of 5, 16, 3, 31 etc. The problem I'm having is finding the square of a decimal like 0.8, 0.08, 0.5, etc.
The first of these sentences puzzles me. How do you find the square root of 3? Do you use the same method for 16? Do you use the same method for 5? Would you use the same method, for a larger number, such as 300 or 30001?

You write as though you know how to work out the square of a whole number. In other words, you could, if you needed to, work out the square of 19. How do you do this? The "obvious" way is by multiplying 19 by 19. If you know how to multiply, are you saying you simply don't know how to multiply numbers that contain a decimal point?

The usual method for doing that is to ignore the decimal point, so that you are multiplying whole numbers. The result will be a whole number. Insert a decimal point into that number so that the number of digits after that decimal point is equal to the total number of digits after the decimal points in the original two numbers whose product you are finding.

Example: find 1.08 × 0.003 by first finding that 108 × 3 = 324, and then convert that to 0.00324 (which has five digits after its decimal point, since 1.08 and 0.003 have a total of five digits after their decimal points). Of course, this method also works for multiplying a number by itself (to find its square).

November 7th, 2009, 07:49 AM   #7
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Quote:
Originally Posted by skipjack
Quote:
 Originally Posted by micheal2345 I understand how to find the square root of 5, 16, 3, 31 etc. The problem I'm having is finding the square of a decimal like 0.8, 0.08, 0.5, etc.
The first of these sentences puzzles me. How do you find the square root of 3? Do you use the same method for 16? Do you use the same method for 5? Would you use the same method, for a larger number, such as 300 or 30001?

You write as though you know how to work out the square of a whole number. In other words, you could, if you needed to, work out the square of 19. How do you do this? The "obvious" way is by multiplying 19 by 19. If you know how to multiply, are you saying you simply don't know how to multiply numbers that contain a decimal point?

The usual method for doing that is to ignore the decimal point, so that you are multiplying whole numbers. The result will be a whole number. Insert a decimal point into that number so that the number of digits after that decimal point is equal to the total number of digits after the decimal points in the original two numbers whose product you are finding.

Example: find 1.08 × 0.003 by first finding that 108 × 3 = 324, and then convert that to 0.00324 (which has five digits after its decimal point, since 1.08 and 0.003 have a total of five digits after their decimal points). Of course, this method also works for multiplying a number by itself (to find its square).
I think he's talking about estimating square roots, not finding what a number would be if it were squared.

 November 7th, 2009, 09:16 AM #8 Senior Member   Joined: Mar 2007 Posts: 428 Thanks: 0 Re: Square Roots I thought aswoods interpreted it right, and gave a good solution.
 November 7th, 2009, 02:15 PM #9 Newbie   Joined: Nov 2009 Posts: 3 Thanks: 0 Re: Square Roots Thank you aswoods, it's much clearer now.
 November 7th, 2009, 03:33 PM #10 Global Moderator   Joined: Dec 2006 Posts: 20,485 Thanks: 2041 What aswoods gave is correct, but not necessarily the best way to proceed. A lot depends on what you're really trying to do. If you're able to find some square roots (of whole numbers, including those you mentioned) to your satisfaction, I remain puzzled as to how you do it; I'm not even sure whether you're finding square roots or squares, but most methods of approximating square roots require you to find squares, and without already knowing how to deal with decimals, it's unclear how you could approximate the square root of 3 or 5 (beyond saying that the first is less than 2, and the second greater than 2).

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# how to find square root of 0.5 without calculator

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