Homeschool Math Blog

I've posted on my site a beginner video lesson on square roots . You can also watch it below: Finding a square root of a number is like finding the side of a square when the area is known. Square root symbol acts as a grouping symbol: anything under it is in parentheses and is solved first. I also solve a few problems involving area & perimeter of squares. I hope it's helpful!

Someone sent me this little mental math trick for square roots. I liked it, didn't know it before, so here goes: I read your suggestion for calculating square root without a calculator. I teach Math for Elementary Teachers and developmental math courses (algebra) to adults. I feel that the focus should be on understanding the number rather than an exercise in following a memorized algorithm. I suggest you have the student determine the pair of perfect squares the number falls between. For example, if finding the sqrt of 645, it falls between the sqrt of 625 which equals 25 and the sqrt of 676 which equals 26. So the sqrt of 645 has to be between 25 and 26. Where does it fall between? There are 50 numbers between 676 and 625. 645 is 20 numbers beyond 625, so 20/50 = 0.4 So the sqrt of 645 is very close to 25.4 This method provides the student with a process that improves their understanding of numbers without expecting them to memorize an algorithm, and it provides an answer to the ...

Is square root of 11 an irrational number? How do you know from using a calculator? Thank you. Well, I happen to know that if the square root of a natural number is NOT a whole number, then it is an irrational number. There are no other possibilities. Of course you can't tell by the calculator. The calculator will show you 8 or 10 decimals, but you won't know from that if it's going to continue or not, or if it is periodical or not. But pure mathematics and established, proven theorems will tell you that! : ) A proof that the square root of 2 is irrational Lots of proofs of the same... plus one proving that any root is irrational if it's not a whole number Proof that the square root of any prime is irrational

prove that 5√ 20 × √ 45 × √ 5 = 150√ 5 This is a quite easy problem. You use two basic "ideas" or properties relating to square roots: * that √ b × b is b - or that you can "pull out" a number times itself from under the root (this is just the definition of a square root of course). * that √ a √ b = √ ab - or you can combine the radicands under the same root when they are multiplied. So √ 20 * √ 45 is equal to √ 20*45 = √ 4 × 5 × 5 × 9 = √ 2 × 2 × 5 × 5 × 3 × 3 = 2 × 5 × 3 = 30. So that's the crux of that problem.

Last week I asked you two questions pertaining to the image below: 1) How does this connect with irrational numbers? Well, the two sides and the diagonal form a right triangle. You can use Pythagorean theorem to find the length of the diagonal. My picture doesn't have any lengths but I was thinking about having the side to be 1 (that's the simplest way). If both sides are 1 and diagonal is d , then Pythagorean theorem says: d 2 = 1 2 + 1 2 Solving that, you get d = √ 2 And, √ 2 is an irrational number. So if the sides of the square are 1, then the diagonal is an irrational number (square root of 2). 2) How does this connect with history of mathematics? Pythagoras was a philosopher in the 6th century B.C. who founded a philosophical school or 'cult' in southern Italy. They had some mystical beliefs, such as reality is mathematical in nature, certain symbols have mystical significance, that the whole cosmos is a scale and a number. Each number had its own personalit...

Two questions for you to think about: 1) How does the above image of a square with one diagonal relate to irrational numbers? 2) How does this image connect with history of mathematics? Answers will be here next week... : )

Studying about Fibonacci numbers and the golden ratio makes an excellent project for high school to write a report on. Besides algebra, it ties in with geometry, botany and art at least. Students do projects and reports in history and English and other school subjects - why not do one or two in math too? The discussion below covers the basics of golden section. I'll try to keep it short. Last time we studied the ratios of a Fibonacci number to the previous Fibonacci number and how they approach a certain number as one continues the sequence - and this certain number is called Phi. Phi is also called the golden section number. You might have heard about it. Even Euclid studied that in ancient times (he called it dividing the line in mean and extreme ratio). This is how we get this golden section or golden cut: Take a line and divide it into two parts, S (short part) and L (Long part). We want the ratio of short part to long part be the same as the ratio of long part to the wh...