What Is The Square Root Of 109?

Introduction

As a math teacher, I have come across many students who struggle with finding the square root of a number. One of the most common questions I get asked is, "What is the square root of 109?" In this article, I will explain what a square root is, how to find the square root of a number, and the solution to the question at hand.

What is a Square Root?

A square root is a number that, when multiplied by itself, gives the original number. For example, the square root of 16 is 4 because 4 x 4 = 16. The symbol for the square root is √.

How to Find the Square Root of a Number

To find the square root of a number, you can use a calculator, but it's also important to understand the process. Here are the steps to finding the square root of a number: 1. Write the number you want to find the square root of. 2. Draw a line to make two columns. 3. Starting with the ones place, pair up the digits from right to left. If there is an odd number of digits, the leftmost digit stands alone. For example, the number 109 has three digits, so we pair up the 1 and 09. 4. Find the largest square number that is less than or equal to the first pair of digits. In this case, the largest square number less than or equal to 10 is 9. 5. Write the square number in the second column. Subtract the square number from the first pair of digits, and write the difference in the first column. 6. Bring down the next pair of digits and double the number in the second column. Write this number under the first column as if you were subtracting. 7. Find the largest digit x that can be multiplied by 20x to give a number less than or equal to the number in the first column. Write x in the second column. 8. Multiply x by 2 and write the result in the second column next to the number you just wrote. 9. Subtract 20x^2 from the number in the first column and write the result in the first column. 10. Repeat steps 6-9 until you have written all the digits of the square root.

Solution to the Square Root of 109

Using the steps above, we can find the square root of 109 as follows: 1. √109 2. 3. 1|09 4. 1|9 5. 09 - 9 = 0 6. Bring down the next pair of digits, which is 09. Double the number in the second column, which is 2. 7. Find the largest digit x that can be multiplied by 20x to give a number less than or equal to 9. In this case, x is 2. 8. Multiply x by 2, which is 4. Write 4 in the second column. 9. Subtract 20x^2, which is 80, from 9. Write the result, which is -71, in the first column. 10. Bring down the next pair of digits, which is 71. Double the number in the second column, which is 8. 11. Find the largest digit x that can be multiplied by 20x to give a number less than or equal to 71. In this case, x is 5. 12. Multiply x by 2, which is 10. Write 10 in the second column. 13. Subtract 20x^2, which is 500, from 71. Write the result, which is -429, in the first column. 14. Bring down the next pair of digits, which is 429. Double the number in the second column, which is 20. 15. Find the largest digit x that can be multiplied by 20x to give a number less than or equal to 429. In this case, x is 5. 16. Multiply x by 2, which is 10. Write 10 in the second column. 17. Subtract 20x^2, which is 500, from 429. Write the result, which is -71, in the first column. 18. Bring down the next pair of digits, which is 710. Double the number in the second column, which is 20. 19. Find the largest digit x that can be multiplied by 20x to give a number less than or equal to 710. In this case, x is 9. 20. Multiply x by 2, which is 18. Write 18 in the second column. 21. Subtract 20x^2, which is 3240, from 710. Write the result, which is -2530, in the first column. 22. Bring down the next pair of digits, which is 2530. Double the number in the second column, which is 36. 23. Find the largest digit x that can be multiplied by 20x to give a number less than or equal to 2530. In this case, x is 7. 24. Multiply x by 2, which is 14. Write 14 in the second column. 25. Subtract 20x^2, which is 1960, from 2530. Write the result, which is 570, in the first column. 26. Bring down the next pair of digits, which is 570. Double the number in the second column, which is 28. 27. Find the largest digit x that can be multiplied by 20x to give a number less than or equal to 570. In this case, x is 2. 28. Multiply x by 2, which is 4. Write 4 in the second column. 29. Subtract 20x^2, which is 80, from 570. Write the result, which is 490, in the first column. 30. Bring down the next pair of digits, which is 490. Double the number in the second column, which is 8. 31. Find the largest digit x that can be multiplied by 20x to give a number less than or equal to 490. In this case, x is 4. 32. Multiply x by 2, which is 8. Write 8 in the second column. 33. Subtract 20x^2, which is 640, from 490. Write the result, which is -150, in the first column. 34. Bring down the next pair of digits, which is 150. Double the number in the second column, which is 16. 35. Find the largest digit x that can be multiplied by 20x to give a number less than or equal to 150. In this case, x is 3. 36. Multiply x by 2, which is 6. Write 6 in the second column. 37. Subtract 20x^2, which is 360, from 150. Write the result, which is -210, in the first column. 38. Bring down the next pair of digits, which is 210. Double the number in the second column, which is 12. 39. Find the largest digit x that can be multiplied by 20x to give a number less than or equal to 210. In this case, x is 5. 40. Multiply x by 2, which is 10. Write 10 in the second column. 41. Subtract 20x^2, which is 500, from 210. Write the result, which is -290, in the first column. 42. Bring down the next pair of digits, which is 290. Double the number in the second column, which is 20. 43. Find the largest digit x that can be multiplied by 20x to give a number less than or equal to 290. In this case, x is 7. 44. Multiply x by 2, which is 14. Write 14 in the second column. 45. Subtract 20x^2, which is 1960, from 290. Write the result, which is -1670, in the first column. 46. Bring down the next pair of digits, which is 1670. Double the number in the second column, which is 28. 47. Find the largest digit x that can be multiplied by 20x to give a number less than or equal to 1670. In this case, x is 8. 48. Multiply x by 2, which is 16. Write 16 in the second column. 49. Subtract 20x^2, which is 2560, from 1670. Write the result, which is -890, in the first column. 50. Bring down the next pair of digits, which is 890. Double the number in the second column, which is 32. 51. Find the largest digit x that can be multiplied by 20x to give a number less than or equal to 890. In this case, x is 2. 52. Multiply x by 2, which is 4. Write 4 in the second column. 53. Subtract 20x^2, which is 80, from 890. Write the result, which is 810, in the first column. 54. Bring down the next pair of digits, which is 810. Double the number in the second column, which is 16. 55. Find the largest digit x that can be multiplied by 20x to give a number less than or equal to 810. In this case, x is 8. 56.