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

3 <p>A number we multiply by itself three times to get the original number is its cube root. It has various uses in real life, such as finding the volume of cube-shaped objects and designing structures. We will now find the cube root of 166375 and explain the methods used.</p>

4 <h2>What is the Cube Root of 166375?</h2>

5 <p>We have learned the definition<a>of</a>the<a>cube</a>root. Now, let’s learn how it is represented using a<a>symbol</a>and<a>exponent</a>. The symbol we use to express the cube root is the radical sign (∛), and the exponent we use is ⅓.</p>

6 <p>In<a>exponential form</a>, ∛166375 is written as 166375(1/3). The cube root is just the opposite operation of finding the cube of a<a>number</a>. For example: Assume ‘y’ as the cube root of 166375, then y³ can be 166375. The cube root of 166375 is an exact value, 55, since 166375 is a<a>perfect cube</a>.</p>

7 <h2>Finding the Cube Root of 166375</h2>

8 <p>Finding the<a>cube root</a>of a number involves identifying the number that must be multiplied three times resulting in the target number. Now, we will go through the different ways to find the cube root of 166375. The common methods we follow to find the cube root are given below:</p>

9 <ul><li>Prime factorization method</li>

10 <li>Approximation method</li>

11 <li>Subtraction method</li>

12 <li>Halley’s method</li>

13 </ul><p>Since 166375 is a perfect cube, the<a>prime factorization</a>method is suitable for finding its cube root.</p>

14 <h3>Cube Root of 166375 by Prime Factorization</h3>

15 <p>Let's find the cube root of 166375 using the prime factorization method.</p>

16 <p>First, factorize 166375 into its prime<a>factors</a>:</p>

17 <p>166375 = 5 × 5 × 5 × 11 × 11 × 11 2.</p>

18 <p>Group the factors into triples: (5 × 5 × 5) and (11 × 11 × 11) 3.</p>

19 <p>Take one factor from each group: 5 and 11 4.</p>

20 <p>Multiply the factors: 5 × 11 = 55</p>

21 <p><strong>The cube root of 166375 is 55.</strong></p>

22 <h3>Explore Our Programs</h3>

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24 <h2>Common Mistakes and How to Avoid Them in the Cube Root of 166375</h2>

23 <h2>Common Mistakes and How to Avoid Them in the Cube Root of 166375</h2>

25 <p>Finding the perfect cube of a number without any errors can be a difficult task for the students. This happens for many reasons. Here are a few mistakes the students commonly make and the ways to avoid them:</p>

24 <p>Finding the perfect cube of a number without any errors can be a difficult task for the students. This happens for many reasons. Here are a few mistakes the students commonly make and the ways to avoid them:</p>

25 + <h2>Download Worksheets</h2>

26 <h3>Problem 1</h3>

27 <p>Imagine you have a cube-shaped toy that has a total volume of 166375 cubic centimeters. Find the length of one side of the box equal to its cube root.</p>

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

29 <p>Side of the cube = ∛166375 = 55 units</p>

30 <h3>Explanation</h3>

31 <p>To find the side of the cube, we need to find the cube root of the given volume.</p>

32 <p>Therefore, the side length of the cube is exactly 55 units.</p>

33 <p>Well explained 👍</p>

34 <h3>Problem 2</h3>

35 <p>A company manufactures 166375 cubic meters of material. Calculate the amount of material left after using 375 cubic meters.</p>

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

37 <p>The amount of material left is 166000 cubic meters.</p>

38 <h3>Explanation</h3>

39 <p>To find the remaining material, we need to subtract the used material from the total amount:</p>

40 <p>166375 - 375 = 166000 cubic meters.</p>

41 <p>Well explained 👍</p>

42 <h3>Problem 3</h3>

43 <p>A bottle holds 166375 cubic meters of volume. Another bottle holds a volume of 5000 cubic meters. What would be the total volume if the bottles are combined?</p>

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

45 <p>The total volume of the combined bottles is 171375 cubic meters.</p>

46 <h3>Explanation</h3>

47 <p>Let’s add the volume of both bottles:</p>

48 <p>166375 + 5000 = 171375 cubic meters.</p>

49 <p>Well explained 👍</p>

50 <h3>Problem 4</h3>

51 <p>When the cube root of 166375 is multiplied by 2, calculate the resultant value. How will this affect the cube of the new value?</p>

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

53 <p>2 × 55 = 110 The cube of 110 = 1331000</p>

54 <h3>Explanation</h3>

55 <p>When we multiply the cube root of 166375 by 2, it results in a significant increase in the volume because the cube increases exponentially.</p>

56 <p>Well explained 👍</p>

57 <h3>Problem 5</h3>

58 <p>Find ∛(46000 + 12000).</p>

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

60 <p>∛(46000 + 12000) = ∛58000 ≈ 38.39</p>

61 <h3>Explanation</h3>

62 <p>As shown in the question ∛(46000 + 12000), we can simplify that by adding them.</p>

63 <p>So, 46000 + 12000 = 58000.</p>

64 <p>Then we use this step:</p>

65 <p>∛58000 ≈ 38.39 to get the answer.</p>

66 <p>Well explained 👍</p>

67 <h2>FAQs on 166375 Cube Root</h2>

68 <h3>1.Can we find the Cube Root of 166375?</h3>

69 <p>Yes, we can find the cube root of 166375 exactly as it is a perfect cube. The cube root is 55.</p>

70 <h3>2.Why is Cube Root of 166375 rational?</h3>

71 <p>The cube root of 166375 is rational because it results in an integer, 55, without any non-repeating<a>decimal</a>part.</p>

72 <h3>3.Is it possible to get the cube root of 166375 as an exact number?</h3>

73 <p>Yes, the cube root of 166375 is an exact number, 55.</p>

74 <h3>4.Can we find the cube root of any number using prime factorization?</h3>

75 <p>The prime factorization method can be used to calculate the cube root of perfect cube numbers effectively. For example, 166375 is a perfect cube, so its cube root can be found precisely using prime factorization.</p>

76 <h3>5.Is there any formula to find the cube root of a number?</h3>

77 <p>Yes, the general<a>formula</a>we use for the cube root of any number ‘a’ is a^(1/3).</p>

78 <h2>Important Glossaries for Cube Root of 166375</h2>

79 <ul><li><strong>Cube root:</strong>The number that is multiplied three times by itself to get the given number is the cube root of that number. </li>

80 <li><strong>Perfect cube: A</strong>number is a perfect cube when it is the product of multiplying a number three times by itself. A perfect cube always results in a whole number. For example: 5 × 5 × 5 = 125, therefore, 125 is a perfect cube. </li>

81 <li><strong>Exponent:</strong>The exponent form of the number denotes the number of times a number can be multiplied by itself. In 166375(1/3), ⅓ is the exponent which denotes the cube root of 166375. </li>

82 <li><strong>Radical sign:</strong>The symbol that is used to represent a root is expressed as (∛). </li>

83 <li><strong>Prime factorization:</strong>A method of expressing a number as the product of its prime factors. This method is particularly useful for finding cube roots of perfect cubes.</li>

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

85 <p>▶</p>

86 <h2>Jaskaran Singh Saluja</h2>

87 <h3>About the Author</h3>

88 <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>

89 <h3>Fun Fact</h3>

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