Finding Square Roots Cube Roots Lesson 1 1

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

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

Square Roots have TWO answers x 2 = 196 What number make 196 when multiplied by itself? √ 196 = ? + 14 BOTH positive & negative answer make 196 so…

Square Roots with Fractions x 2 = 9 256 What number make 9 when multiplied, then what makes 256? 3 √ 9 = ? √ 256 = ? + 16 3 16 BOTH positive & negative answer make 9 & 256 so…

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

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

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

Lets Practice! x 3 = 3, 375 x 2 = 25 169 15 + 5 13 x 2 = 1 + x 3 = 64 343 4 7 1

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

We could estimate it even more if necessary! We could estimate it even more if necessary √ 6 ≈ 2. 5 Choose some numbers between 2 & 3 and square them! 2. 4 = ? = 5. 76 2. 5 = ? = 6. 25 2. 6 = ? = 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!!!)

It gets easier…I PROMISE!!!! √ 10 ≈ ? No number makes 10 when squared…it is an IRRATIONAL number! √ 16 = 4 √ 9 = 3 Find a Perfect Square that is larger and smaller than 6! So the answer must be BETWEEN these two! = 3. 2 Since 10 is pretty much closer to 9 use something like 3. 2 instead

Lets go TWO decimal places now! √ 10 ≈ 3. 2 Choose some numbers between 3 & 4 and square them! But stick closer to 3! 3. 1 = ? 9. 61 3. 2 = ? 10. 24 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!!!)

Practice… √ 21 ≈ ? √ 25 = 5 √ 16 = 4. 5 4. 4 = ? 19. 36 4. 5 = ? 20. 25 4. 6 = ? Now find one more decimal place! √ 21 ≈ 4. 55

Practice… √ 2 ≈ ? √ 4 = 2 √ 1 = 1. 5 1. 4 = ? 1. 96 1. 5 = ? 2. 25 1. 6 = ? Now find one more decimal place! √ 2 ≈ 1. 45

Practice… √ 15 ≈ ? √ 16 = 4 √ 9 = 3. 8 3. 7 = ? 13. 69 3. 8 = ? 14. 44 3. 9 = ? 15. 21 Now find one more decimal place! √ 15 ≈ 3. 85