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Math project Trimester 1
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- Gleiten: 1
- Sis, can you help me learn how to apply radicals and square roots to problem? I need to learn about them for my project
- Lily got home from school and started her homework for Algebra 1. Her little sister,Catherine, walked up to her, who seemed very upset at the moment.
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- Sure, but It’s complicated, you need to know what a square root is first.
- Okay, then explain it!
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- A square root is a number that, when multiplied by itself, equals another number. This is often expressed by using a radical symbol
- √16 = 4 because 4 x 4 = 16√36 = 6 because 6 x 6 = 36√49 = 7 because 7 x 7 = 49√81= 9 because 9 x 9= 81
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- Simplifying Radicals Using Prime Factorization
- √20√2x2x52√5√8√2x2x22√2√48√2x2x2x2x34√3
- Step 1: break down the square root into 2 factors and keep factorizing until you reach a prime numberStep 2: if there are pairs of the same prime numbers, put them outside the square root and put the rest in the square root, if there is more than 1 pair or radical multiply them with each other
- In order to simplify a square root, you have to use prime factorization, which requires the factors of that number
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- Do you want to try some problems out?
- Sure, why not?
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- Adding and subtracting radicals
- Adding and subtracting radicals
- 2 √5 + 4 √5 = 6 √57 √2 - 4 √2 = 3 √22 √7 + 5 √7 = 7 √7
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- Multiplying Radicals
- Example 12 √6 x 3 √42 x 3 and 6 x 46 √12Simplify √12 then multiply by 62 √3 x 6 = 12 √3
- Multiplying radicals is multiplying 2 or more roots together, radicals can only be multiplied by radicals and radicands by radicands.
- She struggled for a while, then showed her. She had written:
- Example 24 √4 x 6 √44 x 6 and √4 x √424 (4) = 96
- When 2 like square roots are multiplied by each other, they cancel each other out and just leave the whole number without the radical
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- Multiply:4 √3 ( 3 + 6 √5)Your answer:4 x 3 = 12 and √3 x 3 = √9 = 34 √3 x 6 √5 = 24 √1512 + 3 + 24 √1515 + 24 √15My answer:4 √3 x 3 = 12 √34 √3 x 6 √5 = 24 √1512 √3 + 24 √15
- That’s not quite right… remember, we can’t multiply radicals by radicands, we can only place the radicand outside the radical
- You can’t multiply the 3 with √3, but you can multiply it with the 4 on the outside
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- Wait, is that all I need to know about radicals?
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- That’s the function of a square root?! Thats so cool!
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- Mom, Lily taught me something new in math, she taught me about radicals! Will I ever actually use it in real life though?
- Well, Catherine, you will probably use it later on if you become an architect or a math major, so maybe
- Later on…
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- To add and subtract radicals, the radicals have to be the same while the radicands (numbers outside) get added and subtracted
- Radicals and Square Roots
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- The square root function is a graph that aligns a number with its square root, you might see it later on! Its formula is f(x) = √x
- Multiply:4 √3 (3 + 6 √5)Your answer :4 x 3 = 12 and 3 x √3 = √9 = 34 x 6 = 24 and √3 x √5 = √1512 + 3 + 24 + √15 = 39 + √15My answer: 4 √3 x 3 = 12 √34 √3 x 6 √ 5 = 24 √1512 √3 + 24 √15
- So far, yes, but I want to show you something else as well.
- This is a square root function. Basically, it takes a number on the graph and aligns it with its square root. Its formula is f(x) = √x
- Today I’ll be presenting my project about radicals and square roots
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