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1 - <p>342 Learners</p>

1 + <p>386 Learners</p>

2 <p>Last updated on<strong>August 5, 2025</strong></p>

3 <p>The cube root of a number is a value that when multiplied thrice by itself results back to the original number. Imagine you have a cube (box) with a known volume. The cube root would then be useful to determine the length of one side of the box.</p>

4 <h2>What is the cube root of 217?</h2>

5 <p>The<a>cube</a>root of 217 is a<a>number</a>, when you multiply it by itself three times, it gives 217. Let’s check a few steps and methods to calculate the cube root of 700.</p>

6 <p>Cube root of 217: ∛217 = 6.006</p>

7 <p>Exponential form of the cube root of 217 is 2171/3</p>

8 <p>Radical form of the cube root of 217 is ∛217 </p>

9 <h2>Finding the Cube Root of 217</h2>

10 <p>Use the following methods to find the<a>cube root</a>of a number:</p>

11 <ul><li>Prime factorization</li>

12 <li>Approximation method</li>

13 <li>Long<a>division</a> </li>

14 <li>Subtraction method</li>

15 <li>Halley’s method - is used when a number is not a<a>perfect cube</a>. </li>

16 </ul><h3>Cube root of 217 using the Halley’s Method</h3>

17 <p>We use the below<a>formula</a>to find the cube root using Halley’s Method:</p>

18 <p>∛a≅ x((x3+2a) / (2x3+a))</p>

19 <p>In the formula, a = given number, 217 x = an approximate number close to the cube root of the number, 217. Let’s say x is 6. Therefore, 63 = 216.</p>

20 <p>Now, let’s apply the formula and find the cube root.</p>

21 <p>Here, a = 217 and x = 6</p>

22 <p>Now apply the formula: </p>

23 <p>∛a≅ x((x3+2a) / (2x3+a))</p>

24 <p>∛217 ≅ 6((63+2 × 217) / (2 × 63+217)) </p>

25 <p>∛217 ≅ 6(( 216+434 ) / (2 x 216 + 217))</p>

26 <p>∛217 ≅ 6((650) / (649))</p>

27 <p>∛217 ≅ 6(1.001)</p>

28 <p>∛217 ≅ 6.006 </p>

29 <h3>Explore Our Programs</h3>

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31 <h2>Common Mistakes and How to Avoid Them in the Cube Root of 217</h2>

30 <h2>Common Mistakes and How to Avoid Them in the Cube Root of 217</h2>

32 <p>While learning cube roots,it’s common for students to make mistakes, to avoid those here are some common mistakes listed below: </p>

31 <p>While learning cube roots,it’s common for students to make mistakes, to avoid those here are some common mistakes listed below: </p>

32 + <h2>Download Worksheets</h2>

33 <h3>Problem 1</h3>

34 <p>Find ∛217 + ∛117?</p>

35 <p>Okay, lets begin</p>

36 <p>∛217 + ∛117</p>

37 <p>= 6.006 + 4.890 </p>

38 <p>= 10.896. </p>

39 <h3>Explanation</h3>

40 <p>To find the solution for ∛217 + ∛117, the value of ∛217 and ∛117 must be found and then added together. The answer is 10.899. </p>

41 <p>Well explained 👍</p>

42 <h3>Problem 2</h3>

43 <p>Solve for x if x³ = 217.</p>

44 <p>Okay, lets begin</p>

45 <p>x3 = 217</p>

46 <p>Value of x = ∛217</p>

47 <p>x = 6.006.</p>

48 <h3>Explanation</h3>

49 <p>To find the value of x, the given value of x3 is to be inverse and the cube root of 217 is to be found. Therefore, the answer will be 6.009. </p>

50 <p>Well explained 👍</p>

51 <h3>Problem 3</h3>

52 <p>The side length ‘s’ of a square is ∛217, find the area of the area of the square.</p>

53 <p>Okay, lets begin</p>

54 <p>Length of a square ‘s’ = ∛217</p>

55 <p>The equation to find the area of square = a2</p>

56 <p>= ∛217 x ∛217</p>

57 <p> = 6.006 × 6.006</p>

58 <p> = 36.072. </p>

59 <h3>Explanation</h3>

60 <p> The formula to find the area of a square is a2, which is ∛217 multiplied twice. Thus, the area of the square is 36.072. </p>

61 <p>Well explained 👍</p>

62 <h2>FAQs For “Cube Root Of 217”</h2>

63 <h3>1.Is 217 divisible by 7?</h3>

64 <p>Yes, 217 is not divisible by 7 as it does not leave any<a>remainder</a>when division is done. 217 ÷ 7 = 31. </p>

65 <h3>2.What is the cube of 217?</h3>

66 <p>The cube of 217 is 217 x 217 x 217 = 10218313. </p>

67 <h3>3.What is the symbol for the cube root?</h3>

68 <p>The<a>symbol</a>that is used to represent the cube root is ∛, is different from the<a>square root</a>symbol as it has 3 on the top left of the radical symbol. </p>

69 <h3>4.What is the prime factorization form of 217?</h3>

70 <h3>5.What is the perfect cube number?</h3>

71 <h2>Important Glossaries for Cube Root of 217</h2>

72 <ul><li><strong>Whole numbers</strong>- The whole numbers are the set of numbers that includes all the positive integers and zero. Example: 0,1,2,3………</li>

73 </ul><ul><li><strong>Square root</strong> -A number’s square root is considered as a number that when it is multiplied by itself gives us the original number.Example: √4 is 2.</li>

74 </ul><ul><li><strong>Exponent</strong>: It is a number which shows how many times a base number should be multiplied by itself.Example: 42= 4 x 4 = 16</li>

75 </ul><ul><li><strong>Irrational number:</strong>The number that cannot be written in the form of a fraction.Example: √2 is an irrational number.</li>

76 </ul><p>What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math</p>

77 <p>▶</p>

78 <h2>Jaskaran Singh Saluja</h2>

79 <h3>About the Author</h3>

80 <p>Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.</p>

81 <h3>Fun Fact</h3>

82 <p>: He loves to play the quiz with kids through algebra to make kids love it.</p>