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2026-01-01
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2026-02-21
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<p>373 Learners</p>
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<p>420 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 49 is the value that, when multiplied by itself three times (cubed), gives the original number 49. Do you know? Cube roots apply to our real life also, like that for measuring dimensions, creating digital art, field of engineering, making financial decisions etc.</p>
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<p>The cube root of 49 is the value that, when multiplied by itself three times (cubed), gives the original number 49. Do you know? Cube roots apply to our real life also, like that for measuring dimensions, creating digital art, field of engineering, making financial decisions etc.</p>
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<h2>What Is the Cube Root of 49?</h2>
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<h2>What Is the Cube Root of 49?</h2>
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<p>The<a>cube</a>root of 49 is 3.65930571002. The cube root of 49 is expressed as ∛49 in radical form, where the “ ∛ ” sign" is called the “radical” sign. In<a>exponential form</a>, it is written as (49)⅓. If “m” is the cube root of 49, then, m3=49. Let us find the value of “m”.</p>
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<p>The<a>cube</a>root of 49 is 3.65930571002. The cube root of 49 is expressed as ∛49 in radical form, where the “ ∛ ” sign" is called the “radical” sign. In<a>exponential form</a>, it is written as (49)⅓. If “m” is the cube root of 49, then, m3=49. Let us find the value of “m”.</p>
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<h2>Finding the Cubic Root of 49</h2>
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<h2>Finding the Cubic Root of 49</h2>
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<p>We can find<a>cube root</a>of 49 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<a>cube root</a>of 49 through a method, named as, Halley’s Method. Let us see how it finds the result. </p>
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<h3>Cubic Root of 49 By Halley’s Method</h3>
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<h3>Cubic Root of 49 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 49.</p>
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<p>Let us apply Halley’s method on the given number 49.</p>
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<p><strong>Step 1:</strong>Let a=49. Let us take x as 3, since, 33=27 is the nearest<a>perfect cube</a>which is<a>less than</a>49.</p>
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<p><strong>Step 1:</strong>Let a=49. Let us take x as 3, since, 33=27 is the nearest<a>perfect cube</a>which is<a>less than</a>49.</p>
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<p><strong>Step 2:</strong>Apply the<a>formula</a>. ∛49≅ 3((33+2×49) / (2(3)3+49))= 3.64…</p>
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<p><strong>Step 2:</strong>Apply the<a>formula</a>. ∛49≅ 3((33+2×49) / (2(3)3+49))= 3.64…</p>
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<p>Hence, 3.64… is the approximate cubic root of 49. </p>
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<p>Hence, 3.64… is the approximate cubic root of 49. </p>
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<h2>Common Mistakes and How to Avoid Them in the Cube Root of 49</h2>
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<h2>Common Mistakes and How to Avoid Them in the Cube Root of 49</h2>
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<p>Understanding common misconceptions or mistakes can make your calculations error free. So let us see how to avoid those from happening.</p>
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<p>Understanding common misconceptions or mistakes can make your calculations error free. So let us see how to avoid those from happening.</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 ((∛98/ ∛49) × (∛98/ ∛49) × (∛98/ ∛49))</p>
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<p>Find ((∛98/ ∛49) × (∛98/ ∛49) × (∛98/ ∛49))</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p> (∛98/ ∛49) × (∛98/ ∛49) × (∛98/ ∛49)</p>
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<p> (∛98/ ∛49) × (∛98/ ∛49) × (∛98/ ∛49)</p>
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<p>= (∛98× ∛98× ∛98) / (∛49× ∛49× ∛49)</p>
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<p>= (∛98× ∛98× ∛98) / (∛49× ∛49× ∛49)</p>
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<p>=((98)⅓)3/ ((49)⅓)3</p>
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<p>=((98)⅓)3/ ((49)⅓)3</p>
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<p>=98/49</p>
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<p>=98/49</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, ∛98=(98)⅓ and ∛49=(49)⅓ , then solved. </p>
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<p> We solved and simplified the exponent part first using the fact that, ∛98=(98)⅓ and ∛49=(49)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 = ∛49, find y³/ y⁶</p>
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<p>If y = ∛49, find y³/ y⁶</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=∛49</p>
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<p> y=∛49</p>
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<p>⇒ y3/y6= (∛49)3 / (∛49)6</p>
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<p>⇒ y3/y6= (∛49)3 / (∛49)6</p>
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<p>⇒ y3/y6= 49/ (49)2= 1/49</p>
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<p>⇒ y3/y6= 49/ (49)2= 1/49</p>
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<p>Answer: 1/49 </p>
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<p>Answer: 1/49 </p>
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<h3>Explanation</h3>
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<h3>Explanation</h3>
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<p>(∛49)3=(491/3)3</p>
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<p>(∛49)3=(491/3)3</p>
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<p>=49, and ∛(49)6</p>
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<p>=49, and ∛(49)6</p>
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<p>=(491/3)6=(49)2.</p>
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<p>=(491/3)6=(49)2.</p>
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<p>Using this, we found the value of y3/y6. </p>
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<p>Using this, we found the value of y3/y6. </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>Multiply ∛49 × ∛64 × ∛125</p>
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<p>Multiply ∛49 × ∛64 × ∛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> ∛49 × ∛64 × ∛125</p>
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<p> ∛49 × ∛64 × ∛125</p>
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<p>= 3.659 × 4 ×5</p>
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<p>= 3.659 × 4 ×5</p>
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<p>= 73.18</p>
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<p>= 73.18</p>
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<p>Answer: 73.18 </p>
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<p>Answer: 73.18 </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 64 is 4 and the cubic root of 125 is 5, hence multiplying ∛125, ∛64 and ∛49. </p>
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<p>We know that the cubic root of 64 is 4 and the cubic root of 125 is 5, hence multiplying ∛125, ∛64 and ∛49. </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 ∛(100)⁶+ ∛(49)⁶ ?</p>
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<p>What is ∛(100)⁶+ ∛(49)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> ∛(1006)+ ∛(49)6 </p>
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<p> ∛(1006)+ ∛(49)6 </p>
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<p>= ((100)6))1/3 +((49)6)1/3</p>
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<p>= ((100)6))1/3 +((49)6)1/3</p>
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<p>=(100)2 + (49)2</p>
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<p>=(100)2 + (49)2</p>
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<p>= 10000 + 2401</p>
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<p>= 10000 + 2401</p>
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<p>Answer: 12401 </p>
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<p>Answer: 12401 </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, ∛100=(100)⅓ and ∛49=(49)⅓ , then solved. </p>
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<p>We solved and simplified the exponent part first using the fact that, ∛100=(100)⅓ and ∛49=(49)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 ∛(49+(-9)+(-13))</p>
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<p>Find ∛(49+(-9)+(-13))</p>
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<p>Okay, lets begin</p>
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<p>Okay, lets begin</p>
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<p> ∛(49-9-13)</p>
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<p> ∛(49-9-13)</p>
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<p>= ∛27</p>
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<p>= ∛27</p>
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<p>=3</p>
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<p>=3</p>
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<p>Answer: 3 </p>
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<p>Answer: 3 </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 49 Cubic Root</h2>
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<h2>FAQs on 49 Cubic Root</h2>
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<h3>1.What is a cube of 49?</h3>
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<h3>1.What is a cube of 49?</h3>
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<p>The answer to the cube of 49 is 117649. </p>
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<p>The answer to the cube of 49 is 117649. </p>
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<h3>2.What is a square root of 49?</h3>
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<h3>2.What is a square root of 49?</h3>
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<h3>3.What is √48 simplified ?</h3>
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<h3>3.What is √48 simplified ?</h3>
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<p>√48 =√(3 ×2×2×2×2) = 4√3. </p>
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<p>√48 =√(3 ×2×2×2×2) = 4√3. </p>
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<h3>4.How to simplify the cube root of 48?</h3>
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<h3>4.How to simplify the cube root of 48?</h3>
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<p>48 is a non-perfect cube, hence you can use the prime factorization method and Halley’s method to simplify it. </p>
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<p>48 is a non-perfect cube, hence you can use the prime factorization method and Halley’s method to simplify it. </p>
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<h3>5.Is 49 a real number?</h3>
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<h3>5.Is 49 a real number?</h3>
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<h2>Important Glossaries for Cubic Root of 49</h2>
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<h2>Important Glossaries for Cubic Root of 49</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. </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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<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>