Finding a Square Root by Reasoning
Date: 11/18/2004 at 10:38:05 From: phil Subject: what is the square root of 40,000,000 What is the square root of 40,000,000? I don't know and it's been bugging me all week.
Date: 11/18/2004 at 12:47:07 From: Doctor Wilko Subject: Re: what is the square root of 40,000,000 Hi Phil, Thanks for writing to Dr. Math! To find the square root of 40,000,000, we need to see if there is a number that when multiplied by itself equals 40,000,000. Instead of going through the formal algebra, I'm just going to reason my way to the answer. Is there a "whole number" that when multiplied by itself equals 40,000,000? I'm just going to guess and check to see. I know that multiplying 2 * 2 will give me the 4, so I'll try 2,000: 2,000 * 2,000 = 4,000,000 (too small by a factor of 10) Now I'll try 20,000: 20,000 * 20,000 = 400,000,000 (too big by a factor of 10) So the answer we want is between those two answers. If we could multiply 2,000 * 2,000 * 10, we would have the correct answer! Now remember that the square root of a number times the square root of that same number is just that number. For example: sqrt(2) * sqrt(2) = 2 Keep that in mind as you see what I do below. 2,000 * 2,000 * sqrt(10) * sqrt(10) = 4,000,000 * 10 = 40,000,000 So the answer to sqrt(40,000,000) is [2,000 * sqrt(10)]. Does this check? Sure, if you multiply [2,000 * sqrt(10)] by itself, you'll get the correct answer. Does this help? Please write back if you need anything else. - Doctor Wilko, The Math Forum http://mathforum.org/dr.math/
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