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☆ Square Root ☆

By David Guerrero. ☆ Square Root ☆. How it works. S quare root: a number that when multiplied by itself equals a given number. Example: The square root of 16 is 4 because 4x4 is 16. B asic S quare Roots. How to find the square root without dividing.

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☆ Square Root ☆

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  1. By David Guerrero ☆ Square Root ☆

  2. How it works Square root: a number that when multiplied by itself equals a given number. Example: The square root of 16 is 4 because 4x4 is 16.

  3. Basic Square Roots

  4. How to find the square root without dividing. • Suppose you want the square root of 75. • 82= 64 and 92 = 81, you know the answer is somewhere between the two. • Try working out 8.52 and you get 72.25 (too small) • Now try 8.62 and you get 73.96 (too small but getting closer) • Now try 8.72 and you get 75.69 (too big) • Now you know the answer is between 8.6 and 8.7 • Now try working out 8.652 and you get 74.8225 (too small) • Now try 8.662 ... and so on. • Keep going until you get an answer that's accurate enough for you.

  5. Square Root Chart

  6. How to find the square root with division. • Again we'll try for the square root of 75. • 82 = 64 and 92 = 81, you know the answer is somewhere between the two. • Guess it's 8.5 then work out 75/8.5 = 8.8235 • Work out the average of 8.5 and 8.8235. It's (8.5 + 8.8235)/2 = 8.66175. This is a very close answer. • To get much closer, work out 75/8.66175 = 8.6588. • Work out the average of 8.66175 and 8.6588 to get 8.660275.

  7. Using a Formula • √X = √S + (X-S)/2√S • X = the number you want the square root of. S = the closest square number you know to X. • Let's try it on the square root of 75 again. • X=75 and so the nearest square number S = 81. This means that √S = 9. • The formula:√75 = 9 + (75-81)/2*9 √75 = 9 + -6/18 = 9 - 0.333 = 8.667

  8. The Number 75 • Look and see if your number will divide by a square number. Here you'll see that 75 will divide by 25 and of course 25= 52. So you can put 75 = 25 x 3 • If you work out the square roots you get sqrt(75) = sqrt(25) x sqrt(3). • sqrt (25)=5 and therefore sqrt(75)= 5 x sqrt3. • You still need to know what sqrt(3) is, but the problem looks simpler now.

  9. Square Root Function

  10. ☆ THE END☆

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