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2026-01-01
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2026-02-28
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<p>198 Learners</p>
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<p>230 Learners</p>
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<p>Last updated on<strong>August 5, 2025</strong></p>
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<p>Last updated on<strong>August 5, 2025</strong></p>
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<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 398 and explain the methods used.</p>
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<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 398 and explain the methods used.</p>
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<h2>What is the Cube Root of 398?</h2>
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<h2>What is the Cube Root of 398?</h2>
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<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. In<a>exponential form</a>, ∛398 is written as 398(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 398, then y3 can be 398. Since the cube root of 398 is not an exact value, we can approximate it to 7.3681.</p>
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<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. In<a>exponential form</a>, ∛398 is written as 398(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 398, then y3 can be 398. Since the cube root of 398 is not an exact value, we can approximate it to 7.3681.</p>
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<h2>Finding the Cube Root of 398</h2>
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<h2>Finding the Cube Root of 398</h2>
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<p>Finding the<a>cube root</a>of a number is to identify 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 398. The common methods we follow to find the cube root are given below: -</p>
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<p>Finding the<a>cube root</a>of a number is to identify 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 398. The common methods we follow to find the cube root are given below: -</p>
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<ol><li>Prime factorization method </li>
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<ol><li>Prime factorization method </li>
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<li>Approximation method </li>
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<li>Approximation method </li>
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<li>Subtraction method </li>
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<li>Subtraction method </li>
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<li>Halley’s method</li>
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<li>Halley’s method</li>
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</ol><p>To find the cube root of a non-<a>perfect cube</a>, we often follow Halley’s method. Since 398 is not a perfect cube, we use Halley’s method.</p>
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</ol><p>To find the cube root of a non-<a>perfect cube</a>, we often follow Halley’s method. Since 398 is not a perfect cube, we use Halley’s method.</p>
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<h2>Cube Root of 398 by Halley’s Method</h2>
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<h2>Cube Root of 398 by Halley’s Method</h2>
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<p>Let's find the cube root of 398 using Halley’s method.</p>
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<p>Let's find the cube root of 398 using Halley’s method.</p>
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<p>The<a>formula</a>is: ∛a ≅ x((x3 + 2a) / (2x3 + a))</p>
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<p>The<a>formula</a>is: ∛a ≅ x((x3 + 2a) / (2x3 + a))</p>
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<p>where: - a = the number for which the cube root is being calculated -</p>
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<p>where: - a = the number for which the cube root is being calculated -</p>
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<p>x = the nearest perfect cube</p>
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<p>x = the nearest perfect cube</p>
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<p>Substituting a = 398; x = 7</p>
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<p>Substituting a = 398; x = 7</p>
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<p>(since 73 = 343 is the nearest perfect cube)</p>
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<p>(since 73 = 343 is the nearest perfect cube)</p>
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<p>∛a ≅ 7((73 + 2 × 398) / (2 × 73 + 398)</p>
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<p>∛a ≅ 7((73 + 2 × 398) / (2 × 73 + 398)</p>
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<p>∛398 ≅ 7((343 + 796) / (686 + 398))</p>
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<p>∛398 ≅ 7((343 + 796) / (686 + 398))</p>
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<p>∛398 ≅ 7.3681</p>
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<p>∛398 ≅ 7.3681</p>
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<p>The cube root of 398 is approximately 7.3681.</p>
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<p>The cube root of 398 is approximately 7.3681.</p>
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<h2>Common Mistakes and How to Avoid Them in the Cube Root of 398</h2>
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<h2>Common Mistakes and How to Avoid Them in the Cube Root of 398</h2>
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<p>Finding the perfect cube of a number without any errors can be a difficult task for students. This happens for many reasons. Here are a few mistakes the students commonly make and ways to avoid them:</p>
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<p>Finding the perfect cube of a number without any errors can be a difficult task for students. This happens for many reasons. Here are a few mistakes the students commonly make and ways to avoid them:</p>
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<h2>Download Worksheets</h2>
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<h3>Problem 1</h3>
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<h3>Problem 1</h3>
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<p>Imagine you have a cube-shaped toy that has a total volume of 398 cubic centimeters. Find the length of one side of the cube equal to its cube root.</p>
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<p>Imagine you have a cube-shaped toy that has a total volume of 398 cubic centimeters. Find the length of one side of the cube equal to its cube root.</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>Side of the cube = ∛398 ≈ 7.37 units</p>
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<p>Side of the cube = ∛398 ≈ 7.37 units</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>To find the side of the cube,</p>
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<p>To find the side of the cube,</p>
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<p>we need to find the cube root of the given volume.</p>
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<p>we need to find the cube root of the given volume.</p>
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<p>Therefore, the side length of the cube is approximately 7.37 units.</p>
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<p>Therefore, the side length of the cube is approximately 7.37 units.</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 2</h3>
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<h3>Problem 2</h3>
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<p>A company manufactures 398 cubic meters of material. Calculate the amount of material left after using 50 cubic meters.</p>
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<p>A company manufactures 398 cubic meters of material. Calculate the amount of material left after using 50 cubic meters.</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The amount of material left is 348 cubic meters.</p>
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<p>The amount of material left is 348 cubic meters.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>To find the remaining material,</p>
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<p>To find the remaining material,</p>
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<p>we need to subtract the used material from the total amount:</p>
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<p>we need to subtract the used material from the total amount:</p>
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<p>398 - 50 = 348 cubic meters.</p>
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<p>398 - 50 = 348 cubic meters.</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 3</h3>
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<h3>Problem 3</h3>
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<p>A container holds 398 cubic meters of liquid. Another container holds a volume of 20 cubic meters. What would be the total volume if the containers are combined?</p>
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<p>A container holds 398 cubic meters of liquid. Another container holds a volume of 20 cubic meters. What would be the total volume if the containers are combined?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>The total volume of the combined containers is 418 cubic meters.</p>
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<p>The total volume of the combined containers is 418 cubic meters.</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Let’s add the volume of both containers:</p>
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<p>Let’s add the volume of both containers:</p>
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<p>398 + 20 = 418 cubic meters.</p>
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<p>398 + 20 = 418 cubic meters.</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 4</h3>
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<h3>Problem 4</h3>
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<p>When the cube root of 398 is multiplied by 3, calculate the resultant value. How will this affect the cube of the new value?</p>
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<p>When the cube root of 398 is multiplied by 3, calculate the resultant value. How will this affect the cube of the new value?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>3 × 7.3681 ≈ 22.1043</p>
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<p>3 × 7.3681 ≈ 22.1043</p>
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<p>The cube of 22.1043 ≈ 10810.9</p>
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<p>The cube of 22.1043 ≈ 10810.9</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Multiplying the cube root of 398 by 3 results in a significant increase in the volume, as the cube of the resultant value increases exponentially.</p>
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<p>Multiplying the cube root of 398 by 3 results in a significant increase in the volume, as the cube of the resultant value increases exponentially.</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h3>Problem 5</h3>
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<h3>Problem 5</h3>
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<p>Find ∛(200 + 198).</p>
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<p>Find ∛(200 + 198).</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>∛(200 + 198) = ∛398 ≈ 7.3681</p>
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<p>∛(200 + 198) = ∛398 ≈ 7.3681</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>As shown in the question ∛(200 + 198),</p>
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<p>As shown in the question ∛(200 + 198),</p>
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<p>we can simplify that by adding them.</p>
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<p>we can simplify that by adding them.</p>
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<p>So, 200 + 198 = 398.</p>
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<p>So, 200 + 198 = 398.</p>
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<p>Then we use this step: ∛398 ≈ 7.3681 to get the answer.</p>
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<p>Then we use this step: ∛398 ≈ 7.3681 to get the answer.</p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h2>FAQs on 398 Cube Root</h2>
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<h2>FAQs on 398 Cube Root</h2>
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<h3>1.Can we find the Cube Root of 398?</h3>
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<h3>1.Can we find the Cube Root of 398?</h3>
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<p>No, we cannot find the cube root of 398 exactly as the cube root of 398 is not a whole number. It is approximately 7.3681.</p>
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<p>No, we cannot find the cube root of 398 exactly as the cube root of 398 is not a whole number. It is approximately 7.3681.</p>
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<h3>2.Why is the Cube Root of 398 irrational?</h3>
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<h3>2.Why is the Cube Root of 398 irrational?</h3>
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<p>The cube root of 398 is irrational because its<a>decimal</a>value goes on without an end and does not repeat.</p>
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<p>The cube root of 398 is irrational because its<a>decimal</a>value goes on without an end and does not repeat.</p>
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<h3>3.Is it possible to get the cube root of 398 as an exact number?</h3>
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<h3>3.Is it possible to get the cube root of 398 as an exact number?</h3>
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<p>No, the cube root of 398 is not an exact number. It is a decimal that is approximately 7.3681.</p>
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<p>No, the cube root of 398 is not an exact number. It is a decimal that is approximately 7.3681.</p>
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<h3>4.Can we find the cube root of any number using prime factorization?</h3>
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<h3>4.Can we find the cube root of any number using prime factorization?</h3>
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<p>The prime factorization method can be used to calculate the cube root of perfect cube numbers, but it is not the right method for non-perfect cube numbers. For example, 2 × 2 × 2 = 8, so 8 is a perfect cube.</p>
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<p>The prime factorization method can be used to calculate the cube root of perfect cube numbers, but it is not the right method for non-perfect cube numbers. For example, 2 × 2 × 2 = 8, so 8 is a perfect cube.</p>
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<h3>5.Is there any formula to find the cube root of a number?</h3>
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<h3>5.Is there any formula to find the cube root of a number?</h3>
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<p>Yes, the formula we use for the cube root of any number ‘a’ is a(1/3).</p>
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<p>Yes, the formula we use for the cube root of any number ‘a’ is a(1/3).</p>
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<h2>Important Glossaries for Cube Root of 398</h2>
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<h2>Important Glossaries for Cube Root of 398</h2>
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<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>
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<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>
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</ul><ul><li><strong>Perfect cube:</strong>A 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: 2 × 2 × 2 = 8; therefore, 8 is a perfect cube. </li>
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</ul><ul><li><strong>Perfect cube:</strong>A 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: 2 × 2 × 2 = 8; therefore, 8 is a perfect cube. </li>
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</ul><ul><li><strong>Exponent:</strong>The exponent form of a number denotes the number of times a number can be multiplied by itself. In 398(1/3), ⅓ is the exponent, which denotes the cube root of 398. </li>
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</ul><ul><li><strong>Exponent:</strong>The exponent form of a number denotes the number of times a number can be multiplied by itself. In 398(1/3), ⅓ is the exponent, which denotes the cube root of 398. </li>
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</ul><ul><li><strong>Radical sign:</strong>The symbol that is used to represent a root which is expressed as (∛). </li>
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</ul><ul><li><strong>Radical sign:</strong>The symbol that is used to represent a root which is expressed as (∛). </li>
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</ul><ul><li><strong>Irrational number:</strong>Numbers that cannot be put in fractional forms are irrational. For example, the cube root of 398 is irrational because its decimal form goes on continuously without repeating the numbers.</li>
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</ul><ul><li><strong>Irrational number:</strong>Numbers that cannot be put in fractional forms are irrational. For example, the cube root of 398 is irrational because its decimal form goes on continuously without repeating the numbers.</li>
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</ul><p>What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math</p>
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</ul><p>What Is Algebra? 🧮 | Simple Explanation with 🎯 Cool Examples for Kids | ✨BrightCHAMPS Math</p>
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<p>▶</p>
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<p>▶</p>
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<h2>Jaskaran Singh Saluja</h2>
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<h2>Jaskaran Singh Saluja</h2>
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<h3>About the Author</h3>
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<h3>About the Author</h3>
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<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>
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<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>
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<h3>Fun Fact</h3>
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<h3>Fun Fact</h3>
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<p>: He loves to play the quiz with kids through algebra to make kids love it.</p>
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<p>: He loves to play the quiz with kids through algebra to make kids love it.</p>