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2026-01-01
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2026-02-28
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<p>417 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>The cube root of 250 is the value which, when multiplied by itself three times (cubed), gives the original number 250. Do you know? Cube roots apply to our real life also, like that for measuring dimensions, density and mass, creating unique digital art etc.</p>
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<p>The cube root of 250 is the value which, when multiplied by itself three times (cubed), gives the original number 250. Do you know? Cube roots apply to our real life also, like that for measuring dimensions, density and mass, creating unique digital art etc.</p>
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<h2>What Is the Cubic Root of 250?</h2>
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<h2>What Is the Cubic Root of 250?</h2>
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<p>The<a>cube</a>root of 250 is 6.29960524947. The cube root of 250 is expressed as ∛250 in radical form, where the “ ∛ “ sign" is called the “radical” sign. In<a>exponential form</a>, it is written as (250)1/3. If “m” is the cube root of 250, then, m3=250. Let us find the value of “m”. </p>
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<p>The<a>cube</a>root of 250 is 6.29960524947. The cube root of 250 is expressed as ∛250 in radical form, where the “ ∛ “ sign" is called the “radical” sign. In<a>exponential form</a>, it is written as (250)1/3. If “m” is the cube root of 250, then, m3=250. Let us find the value of “m”. </p>
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<h2>Finding the Cube Root of 250</h2>
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<h2>Finding the Cube Root of 250</h2>
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<p>The<a>cube root</a>of 250 is expressed as 5∛2 as its simplest radical form, since</p>
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<p>The<a>cube root</a>of 250 is expressed as 5∛2 as its simplest radical form, since</p>
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<p> 250 = 5×5×5×2</p>
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<p> 250 = 5×5×5×2</p>
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<p>∛250 = ∛(5×5×5×2)</p>
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<p>∛250 = ∛(5×5×5×2)</p>
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<p>Group together three same<a>factors</a>at a time and put the remaining factor under ∛ .</p>
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<p>Group together three same<a>factors</a>at a time and put the remaining factor under ∛ .</p>
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<p>∛250= 5∛2 </p>
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<p>∛250= 5∛2 </p>
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<p> We can find cube roots of 250 through a method, named as, Halley’s Method. Let us see how it finds the result. </p>
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<p> We can find cube roots of 250 through a method, named as, Halley’s Method. Let us see how it finds the result. </p>
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<h3>Cube Root of 250 By Halley’s Method</h3>
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<h3>Cube Root of 250 By Halley’s Method</h3>
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<p>Now, what is Halley’s Method? It is an iterative method for finding cube roots of a given<a>number</a>N, such that, x3=N, where this method approximates the value of “x”.</p>
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<p>Now, what is Halley’s Method? It is an iterative method for finding cube roots of a given<a>number</a>N, such that, x3=N, where this method approximates the value of “x”.</p>
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<p>Formula is ∛a≅ x((x3+2a) / (2x3+a)), where </p>
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<p>Formula is ∛a≅ x((x3+2a) / (2x3+a)), where </p>
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<p>a=given number whose cube root you are going to find</p>
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<p>a=given number whose cube root you are going to find</p>
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<p>x=<a>integer</a>guess for the cubic root</p>
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<p>x=<a>integer</a>guess for the cubic root</p>
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<p>Let us apply Halley’s method on the given number 250.</p>
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<p>Let us apply Halley’s method on the given number 250.</p>
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<p><strong>Step 1:</strong>Let a=250. Let us take x as 6, since 63=216 is the nearest<a>perfect cube</a>which is<a>less than</a>250.</p>
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<p><strong>Step 1:</strong>Let a=250. Let us take x as 6, since 63=216 is the nearest<a>perfect cube</a>which is<a>less than</a>250.</p>
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<p><strong>Step 2:</strong>Apply the<a>formula</a>. ∛250≅ 6((63+2×250) / (2(6)3+250))= 6.29…</p>
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<p><strong>Step 2:</strong>Apply the<a>formula</a>. ∛250≅ 6((63+2×250) / (2(6)3+250))= 6.29…</p>
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<p>Hence, 6.29… is the approximate cubic root of 250. </p>
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<p>Hence, 6.29… is the approximate cubic root of 250. </p>
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<h2>Common Mistakes and How to Avoid Them in the Cube Root of 250</h2>
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<h2>Common Mistakes and How to Avoid Them in the Cube Root of 250</h2>
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<p>some mistakes with their solutions given :</p>
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<p>some mistakes with their solutions given :</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>Find ∛250/ ∛240</p>
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<p>Find ∛250/ ∛240</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p> ∛250/ ∛240</p>
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<p> ∛250/ ∛240</p>
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<p>= 6.299 / 6.214</p>
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<p>= 6.299 / 6.214</p>
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<p>= 6299/6214</p>
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<p>= 6299/6214</p>
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<p>=1.014</p>
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<p>=1.014</p>
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<p>Answer: 1.014 </p>
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<p>Answer: 1.014 </p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>We found that the cubic root of 240 is 6.214…, hence dividing ∛250 by ∛240. </p>
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<p>We found that the cubic root of 240 is 6.214…, hence dividing ∛250 by ∛240. </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>The Volume of a cube is 250 cubic centimeters, find the length of one side of the cube.</p>
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<p>The Volume of a cube is 250 cubic centimeters, find the length of one side of the cube.</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p>We know that, (side of a cube)3=Volume of a cube</p>
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<p>We know that, (side of a cube)3=Volume of a cube</p>
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<p>⇒side of the cube = ∛(Volume of the cube)</p>
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<p>⇒side of the cube = ∛(Volume of the cube)</p>
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<p>⇒side of the cube = ∛250</p>
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<p>⇒side of the cube = ∛250</p>
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<p>⇒ side of the cube = 6.299 cm</p>
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<p>⇒ side of the cube = 6.299 cm</p>
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<p>Answer: 6.299 cm </p>
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<p>Answer: 6.299 cm </p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>We applied the formula for finding the volume of a cube, and inverted it to find the measure of one side of the cube. </p>
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<p>We applied the formula for finding the volume of a cube, and inverted it to find the measure of one side of the cube. </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>Subtract ∛250 - ∛216, ∛343-∛250</p>
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<p>Subtract ∛250 - ∛216, ∛343-∛250</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p> ∛250-∛216= 6.299-6= 0.299</p>
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<p> ∛250-∛216= 6.299-6= 0.299</p>
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<p>∛343-∛250 = 7-6.299 = 0.701</p>
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<p>∛343-∛250 = 7-6.299 = 0.701</p>
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<p>Answer: 0.299, 0.701 </p>
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<p>Answer: 0.299, 0.701 </p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>We know that the cubic root of 216 is 6, hence subtracting ∛216 from ∛250. Applying the same for the next one, we know that the cubic root of 343 is 7, hence subtracting ∛250 from ∛343. </p>
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<p>We know that the cubic root of 216 is 6, hence subtracting ∛216 from ∛250. Applying the same for the next one, we know that the cubic root of 343 is 7, hence subtracting ∛250 from ∛343. </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>What is ∛(250²) ?</p>
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<p>What is ∛(250²) ?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p> ∛(2502) = ∛62500 = 39.685… </p>
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<p> ∛(2502) = ∛62500 = 39.685… </p>
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<p>Answer: 39.685 </p>
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<p>Answer: 39.685 </p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>We first found the square value of 250, which is 62500, and then found out the cube root of 62500. </p>
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<p>We first found the square value of 250, which is 62500, and then found out the cube root of 62500. </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 ∛((250+93)×(250+262)).</p>
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<p>Find ∛((250+93)×(250+262)).</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p> ∛((250+93)×(250+262))</p>
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<p> ∛((250+93)×(250+262))</p>
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<p>= ∛(343×512)</p>
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<p>= ∛(343×512)</p>
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<p>=∛((7)3 × (8)3)</p>
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<p>=∛((7)3 × (8)3)</p>
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<p>=∛73 × ∛83</p>
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<p>=∛73 × ∛83</p>
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<p>= 7 × 8</p>
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<p>= 7 × 8</p>
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<p>=56</p>
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<p>=56</p>
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<p>Answer: 56 </p>
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<p>Answer: 56 </p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>Simplified the expression, and found out the cubic root of the result. </p>
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<p>Simplified the expression, and found out the cubic root of the result. </p>
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<p>Well explained 👍</p>
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<p>Well explained 👍</p>
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<h2>FAQs on 250 Cube Root</h2>
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<h2>FAQs on 250 Cube Root</h2>
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<h3>1.What is the simplest form of 3√250 ?</h3>
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<h3>1.What is the simplest form of 3√250 ?</h3>
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<p> 3√250 = 3√(5×5×5×2) = 3×5√10 =15√10. </p>
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<p> 3√250 = 3√(5×5×5×2) = 3×5√10 =15√10. </p>
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<h3>2.What number cube is 250?</h3>
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<h3>2.What number cube is 250?</h3>
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<p>: (5∛2)3 = 250. Hence, 5∛2, when cubed, gives 250.</p>
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<p>: (5∛2)3 = 250. Hence, 5∛2, when cubed, gives 250.</p>
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<h3>3.Is 250 a square root?</h3>
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<h3>3.Is 250 a square root?</h3>
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<h3>4.How to find the cube root of 255?</h3>
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<h3>4.How to find the cube root of 255?</h3>
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<p>The cube root of 255 is the value which, when multiplied by itself three times (cubed), gives the original number, 255. So, cube roots can be found through prime factorization method or Halley’s method. The value of ∛255 is 6.34…</p>
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<p>The cube root of 255 is the value which, when multiplied by itself three times (cubed), gives the original number, 255. So, cube roots can be found through prime factorization method or Halley’s method. The value of ∛255 is 6.34…</p>
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<h3>5.Is the ∛250 irrational?</h3>
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<h3>5.Is the ∛250 irrational?</h3>
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<p>Yes, ∛250=6.29… is an irrational number, since it cannot be expressed in the form p/q, where p and q are integers and q≠0. </p>
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<p>Yes, ∛250=6.29… is an irrational number, since it cannot be expressed in the form p/q, where p and q are integers and q≠0. </p>
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<h2>Important Glossaries for Cube Root of 250</h2>
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<h2>Important Glossaries for Cube Root of 250</h2>
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<ul><li><strong>Irrational Numbers -</strong>Numbers which cannot be expressed as p/q, where p and q are integers and q not equal to 0 are called Irrational numbers. </li>
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<ul><li><strong>Irrational Numbers -</strong>Numbers which cannot be expressed as p/q, where p and q are integers and q not equal to 0 are called Irrational numbers. </li>
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</ul><ul><li><strong>Whole numbers -</strong>The whole numbers are part of the number system, which includes all the positive integers from 0 to infinity. These cannot be in fractional or decimal form. </li>
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</ul><ul><li><strong>Whole numbers -</strong>The whole numbers are part of the number system, which includes all the positive integers from 0 to infinity. These cannot be in fractional or decimal form. </li>
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</ul><ul><li><strong>Square root -</strong>The square root of a number is a value, which, on multiplication by itself, gives the original number, such that √x = y, where y×y = x.</li>
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</ul><ul><li><strong>Square root -</strong>The square root of a number is a value, which, on multiplication by itself, gives the original number, such that √x = y, where y×y = x.</li>
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</ul><ul><li><strong>Polynomial -</strong>It is an algebraic expression made up of variables like “x” and constants, combined using addition, subtraction, multiplication, or division, where the variables are raised to whole number exponents.</li>
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</ul><ul><li><strong>Polynomial -</strong>It is an algebraic expression made up of variables like “x” and constants, combined using addition, subtraction, multiplication, or division, where the variables are raised to whole number exponents.</li>
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</ul><ul><li><strong>Approximation -</strong>Finding out a value which is nearly correct, but not perfectly correct, as if the approximate value is just near and close to the original value.</li>
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</ul><ul><li><strong>Approximation -</strong>Finding out a value which is nearly correct, but not perfectly correct, as if the approximate value is just near and close to the original value.</li>
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</ul><ul><li><strong>Iterative method -</strong>This method is a process, used in mathematics, which uses an initial value to generate further and step-by-step sequence of solutions for a problem.</li>
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</ul><ul><li><strong>Iterative method -</strong>This method is a process, used in mathematics, which uses an initial value to generate further and step-by-step sequence of solutions for a problem.</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>