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Part of the Lesson Stem Teachers Script Hello Mathematicians. After Part of the Stem Teachers Script Lesson In this lesson you Introduction Hello mathematicians. After today's lesson, you will be able to simplify expressions are going to involving square roots. learn…by 10-20 sec doing/using… You remember that the square root of a number is the side length of a square with an area equal to that number. So the square root of 16 is 4 because a square with an area of 16 would have a side length of 4. Since all sides of a square are the same Connection length, finding the square root of a number, "A" means finding some number that when multiplied by itself gives you A. So the square root of 25 is 5 because 5 times (Define Terms/ itself is 25. Building on Prior You know that… Knowledge) 30-60 sec Also remember that while all numbers greater than zero have a square root, only numbers called, "perfect squares," have integer square roots. Trying to take the square root of a number that is not a perfect square results in an irrational number. So 18 is not a perfect square because 4 times itself is 16, 5 times itself is 25, which means the square root of 18 is an irrational number greater than 4 but less than 5. Demonstration I’m going to But sometimes it is possible and very useful to simplify square roots into smaller explain this idea terms. We will simplify radical 18 in just a minute, but first I want you to think about 1-3 minc by showing you¦ something. Radical 4 is 2, and radical 9 is 3. When I multiply radical 4 times radical 9, I get radicaly 36, which you know is 6. Now thinking about this backwards, I could start with radical 36, and break it up into two of its factors, radical 4 times radical 9. That would give me 2 times 3, which is 6...exactly what we know radical 36 to be. This could help you break down numbers that you may not know are perfect squares, such as 400. If you think about it, both 4 and 100 are perfect squares and they are a factor pair of 400. So you could split radical 400 into radical 4 times radical 100. This is 2 times 10, which is 20. So 400 is a perfect square and its square root is 20. This idea can also help us simplify radical 18. Since 18 is not a perfect square, we will not be able to eliminate the radical completely. But we can make it simpler. Can you think of any factors of 18 that are perfect squares? 9 is right? 9 times what is 18? 9 times 2. So I can split radical 18 into radical 9 times radical 2. And since I know radical 9 is 3, I can rewrite this as 3 times radical 2. Radical 2 is an irrational number, so I cannot simplify it any further. Let's try another. Radical 24. Can you think of any perfect square factors of 24? 4 is. So I rewrite radical 24 as radical 4 times radical 6. Radical 4 is 2, so I get 2 radical 6. Here's one more: Radical 30. Can you think of any perfect square factors of 30? Well, it definitely has factors...such as 3 and 10. But neither of those is a perfect square, so splitting it up this way does not help us simplify radical 30. I could try 5 and 6, but neither of those is a perfect square. Radical 30 is actually as simple as you can make it. Radical 50 Radical 1600 Application Let’s see how this works in a 1-2 min problem¦ Radical 70 Radical 80 Conclusion Now you can simplify expressions involving square roots. So, now you know how to…by… 10-20 sec .
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