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Finding Square Roots & Cube Roots

Finding Square Roots & Cube Roots. Lesson 1.1 part 3. Squares and Square Roots. 5 2 = ?. 25. √25 = ?. 5. 8 2 = ?. 64. √64 = ?. 8. 12 2 = ?. 144. √144 = ?. 12. Notice that they are Inverses of each other!. Square Roots have TWO answers. x 2 = 196.

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Finding Square Roots & Cube Roots

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  1. Finding Square Roots & Cube Roots Lesson 1.1 part 3

  2. Squares and Square Roots 52 = ? 25 √25 = ? 5 82 = ? 64 √64 = ? 8 122 = ? 144 √144 = ? 12 Notice that they are Inverses of each other!

  3. Square Roots have TWO answers x2 = 196 What number make 196 when multiplied by itself? √196 = ? + 14 BOTH positive & negative answer make 196 so…

  4. Square Roots with Fractions 3 √9 = ? x2 = 9 256 √256 = ? 16 What number make 9 when multiplied, then what makes 256? 3 16 + BOTH positive & negative answer make 9 & 256 so…

  5. Cube Roots are a little different… 8 x 8 = 64 64 x 8 = 512 3 √512 = ? x3 = 512 Put a little 3 in the corner of the square root box! = 8 What number makes 512 when multiplied by itself THREE times??? BUT…only the POSITIVE version… -8 x (-8) = 64 64 x (-8) = -512

  6. Cube Roots with Fractions 4 x 4 = 16 16 x 4 = 64 3 √64 = ? x3 = 64 343 3 7 x 7 = 49 49 x 7 = 343 √343 = ? Remember to multiply a number THREE times! 4 7 Again…only the POSITIVE answers work!!!

  7. Lets Practice! x2 = 9 49 x2 = 324 + 18 3 7 + x3 = 8 125 2 5 x3 = 216 6

  8. Lets Practice! x2 = 1 + 1 x3 = 3,375 15 5 13 x2 = 25 169 x3 = 64 343 4 7 +

  9. Estimating Square Roots √9 = 3 √6 ≈ ? So the answer must be BETWEEN these two! No number makes 6 when squared…it is an IRRATIONAL number! √4 = 2 = 2.5 If right in the middle .5 If closer to small number .2 If closer to big number .8 Find a Perfect Square that is larger and smaller than 6!

  10. We could estimate it even more if necessary! 2.4 = ? = 5.76 We could estimate it even more if necessary √6 ≈ 2.5 2.5 = ? = 6.25 2.6 = ? Choose some numbers between 2 & 3 and square them! = 6.76 Now, which answers is 6.0 between???? √6 ≈ 2.45 Since it falls between 2.4 and 2.5 do 2.45 (its between the two!!!)

  11. It gets easier…I PROMISE!!!! √16 = 4 √10 ≈ ? So the answer must be BETWEEN these two! No number makes 10 when squared…it is an IRRATIONAL number! √9 = 3 = 3.2 Since 10 is pretty much closer to 9 use something like 3.2 instead Find a Perfect Square that is larger and smaller than 6!

  12. Lets go TWO decimal places now! 3.1 = ? 9.61 √10 ≈ 3.2 3.2 = ? 10.24 Choose some numbers between 3 & 4 and square them! But stick closer to 3! 3.3 = ? I found my answer already! √10 ≈ 3.15 Since it falls between 3.1 and 3.2 do 3.15 (its between the two!!!)

  13. Practice… 19.36 4.4 = ? √25 = 5 √21 ≈ ? 4.5 = ? = 4.5 20.25 √16 = 4 4.6 = ? Now find one more decimal place! √21 ≈ 4.55

  14. Practice… 1.96 1.4 = ? √4 = 2 √2 ≈ ? 2.25 1.5 = ? = 1.5 √1 = 1 1.6 = ? Now find one more decimal place! √2 ≈ 1.45

  15. Practice… 13.69 3.7 = ? √16 = 4 √15 ≈ ? 3.8 = ? = 3.8 14.44 √9 = 3 3.9 = ? 15.21 Now find one more decimal place! √15 ≈ 3.85

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