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2026-01-01
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<p>607 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 128 is the value that, when multiplied by itself three times (cubed), gives the original number 128. Do you know? Cube roots apply to our real life also, like that for measuring dimensions, density and mass, field of engineering etc.</p>
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<p>The cube root of 128 is the value that, when multiplied by itself three times (cubed), gives the original number 128. Do you know? Cube roots apply to our real life also, like that for measuring dimensions, density and mass, field of engineering etc.</p>
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<h2>What Is the Cube Root of 128?</h2>
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<h2>What Is the Cube Root of 128?</h2>
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<p>The<a>cube</a>root of 128 is 5.03968419958. The cube root of 128 is expressed as ∛128 in radical form, where the “∛" sign is called the “radical” sign.</p>
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<p>The<a>cube</a>root of 128 is 5.03968419958. The cube root of 128 is expressed as ∛128 in radical form, where the “∛" sign is called the “radical” sign.</p>
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<p>In<a>exponential form</a>, it is written as (128)⅓. If “m” is the cube root of 128, then, m3=128. Let us find the value of “m”. </p>
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<p>In<a>exponential form</a>, it is written as (128)⅓. If “m” is the cube root of 128, then, m3=128. Let us find the value of “m”. </p>
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<h2>Finding the Cube Root of 128</h2>
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<h2>Finding the Cube Root of 128</h2>
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<p>The<a>cube root</a>of 128 is expressed as 4∛2 as its simplest radical form,</p>
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<p>The<a>cube root</a>of 128 is expressed as 4∛2 as its simplest radical form,</p>
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<p>since 128 = 2×2×2×2×2×2×2</p>
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<p>since 128 = 2×2×2×2×2×2×2</p>
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<p>∛128 = ∛(2×2×2×2×2×2×2)</p>
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<p>∛128 = ∛(2×2×2×2×2×2×2)</p>
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<p>Group together three same<a>factors</a>at a time and put the remaining factor under the ∛ .</p>
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<p>Group together three same<a>factors</a>at a time and put the remaining factor under the ∛ .</p>
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<p>∛128= 4∛2 </p>
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<p>∛128= 4∛2 </p>
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<p> We can find cube root of 128 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 root of 128 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 128 By Halley’s Method</h3>
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<h3>Cube Root of 128 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 128.</p>
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<p> Let us apply Halley’s method on the given number 128.</p>
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<p><strong>Step 1:</strong>Let a=128. Let us take x as 5, since, 53=125 is the nearest<a>perfect cube</a>which is<a>less than</a>128.</p>
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<p><strong>Step 1:</strong>Let a=128. Let us take x as 5, since, 53=125 is the nearest<a>perfect cube</a>which is<a>less than</a>128.</p>
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<p><strong>Step 2</strong>: Apply the<a>formula</a>. ∛128≅ 5((53+2×128) / (2(5)3+128))= 5.039…</p>
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<p><strong>Step 2</strong>: Apply the<a>formula</a>. ∛128≅ 5((53+2×128) / (2(5)3+128))= 5.039…</p>
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<p>Hence, 5.039… is the approximate cubic root of 128. </p>
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<p>Hence, 5.039… is the approximate cubic root of 128. </p>
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<h2>Common Mistakes and How to Avoid Them in the Cubic Root of 128</h2>
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<h2>Common Mistakes and How to Avoid Them in the Cubic Root of 128</h2>
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<p>some common mistakes and their solutions are given below:</p>
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<p>some common mistakes and their solutions are given below:</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 (∛128/ ∛64) × (∛128/ ∛64) × (∛128/ ∛64)</p>
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<p>Find (∛128/ ∛64) × (∛128/ ∛64) × (∛128/ ∛64)</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p> (∛128/ ∛64) × (∛128/ ∛64) × (∛128/ ∛64)</p>
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<p> (∛128/ ∛64) × (∛128/ ∛64) × (∛128/ ∛64)</p>
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<p>= (∛128× ∛128× ∛128) / (∛64× ∛64× ∛64)</p>
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<p>= (∛128× ∛128× ∛128) / (∛64× ∛64× ∛64)</p>
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<p>=((128)⅓)3/ ((64)⅓)3</p>
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<p>=((128)⅓)3/ ((64)⅓)3</p>
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<p>=128/64</p>
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<p>=128/64</p>
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<p>= 2</p>
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<p>= 2</p>
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<p>Answer: 2 </p>
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<p>Answer: 2 </p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>We solved and simplified the exponent part first using the fact that, ∛128=(128)⅓ and ∛64=(64)⅓ , then solved. </p>
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<p>We solved and simplified the exponent part first using the fact that, ∛128=(128)⅓ and ∛64=(64)⅓ , then solved. </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>If y = ∛128, find y^3.</p>
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<p>If y = ∛128, find y^3.</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p> y=∛128</p>
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<p> y=∛128</p>
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<p>⇒ y3= (∛128)3 </p>
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<p>⇒ y3= (∛128)3 </p>
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<p>⇒ y3= 128</p>
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<p>⇒ y3= 128</p>
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<p>Answer: 128 </p>
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<p>Answer: 128 </p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p> (∛128)3=(1281/3)3=128.</p>
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<p> (∛128)3=(1281/3)3=128.</p>
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<p>Using this, we found the value of y3. </p>
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<p>Using this, we found the value of y3. </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 ∛128 - ∛125</p>
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<p>Subtract ∛128 - ∛125</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p> ∛128-∛125</p>
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<p> ∛128-∛125</p>
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<p>= 5.039-5</p>
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<p>= 5.039-5</p>
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<p>= 0.039</p>
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<p>= 0.039</p>
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<p>Answer: 0.039 </p>
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<p>Answer: 0.039 </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 125 is 5, hence subtracting ∛125 from ∛128. </p>
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<p>We know that the cubic root of 125 is 5, hence subtracting ∛125 from ∛128. </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 ∛(128^6) ) ?</p>
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<p>What is ∛(128^6) ) ?</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p> ∛(1286)</p>
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<p> ∛(1286)</p>
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<p>= ((128)6))1/3</p>
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<p>= ((128)6))1/3</p>
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<p>=( 128)2</p>
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<p>=( 128)2</p>
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<p>= 16384</p>
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<p>= 16384</p>
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<p>Answer: 16384</p>
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<p>Answer: 16384</p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>We solved and simplified the exponent part first using the fact that, ∛128=(128)⅓, then solved. </p>
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<p>We solved and simplified the exponent part first using the fact that, ∛128=(128)⅓, then solved. </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 ∛(128+(-3))</p>
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<p>Find ∛(128+(-3))</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p> ∛(128-3)</p>
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<p> ∛(128-3)</p>
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<p>= ∛125</p>
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<p>= ∛125</p>
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<p>= 5</p>
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<p>= 5</p>
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<p>Answer: 5 </p>
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<p>Answer: 5 </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 128 Cube Root</h2>
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<h2>FAQs on 128 Cube Root</h2>
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<h3>1.∛128 lies between which two perfect cubes?</h3>
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<h3>1.∛128 lies between which two perfect cubes?</h3>
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<p>∛128=5.03… lies between perfect cubes 1 and 8.</p>
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<p>∛128=5.03… lies between perfect cubes 1 and 8.</p>
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<h3>2.What are the factors of 128?</h3>
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<h3>2.What are the factors of 128?</h3>
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<p> The factors of 128 are 1,2,4,8,16,32,64 and 128. </p>
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<p> The factors of 128 are 1,2,4,8,16,32,64 and 128. </p>
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<h3>3.What is the simplest form of ∛108?</h3>
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<h3>3.What is the simplest form of ∛108?</h3>
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<p>108 = 2×2×3×3×3</p>
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<p>108 = 2×2×3×3×3</p>
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<p>∛108 = ∛(2×2×3×3×3)</p>
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<p>∛108 = ∛(2×2×3×3×3)</p>
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<p>∛108= 3∛4</p>
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<p>∛108= 3∛4</p>
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<p>3∛4 is the simplest radical form of 108 </p>
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<p>3∛4 is the simplest radical form of 108 </p>
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<h3>4.Is 108 a perfect cube?</h3>
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<h3>4.Is 108 a perfect cube?</h3>
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<p> No, 108 is not a perfect cube. </p>
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<p> No, 108 is not a perfect cube. </p>
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<h3>5.Is 72 a perfect square?</h3>
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<h3>5.Is 72 a perfect square?</h3>
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<h2>Important Glossaries for Cubic Root of 128</h2>
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<h2>Important Glossaries for Cubic Root of 128</h2>
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<ul><li><strong>Integers: </strong>Integers can be a positive natural number, negative of a positive number, or zero. We can perform all the arithmetic operations on integers. The examples of integers are, 1, 2, 5,8, -8, -12, etc.</li>
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<ul><li><strong>Integers: </strong>Integers can be a positive natural number, negative of a positive number, or zero. We can perform all the arithmetic operations on integers. The examples of integers are, 1, 2, 5,8, -8, -12, etc.</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. </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. </li>
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</ul><ul><li><strong>Square root:</strong>The square root of a number is a value “y” such that when “y” is multiplied by itself → y ⤫ y, the result is the original number.</li>
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</ul><ul><li><strong>Square root:</strong>The square root of a number is a value “y” such that when “y” is multiplied by itself → y ⤫ y, the result is the original number.</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.</li>
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</ul><ul><li><strong>Approximation:</strong> Finding out a value which is nearly correct, but not perfectly correct.</li>
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</ul><ul><li><strong>Iterative method:</strong>This method is a mathematical process 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 mathematical process 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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<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>