Question

what is the cube root of 4 17/27 (4 Whole number 17/27​

Answer 1

Answer:

it help for you I hope you like

Step-by-step explanation:

3√4 17

27

=3√125/27

=5/3 ans.

Answer 2

$\large\underline{\sf{Solution-}}$

Given expression is

$\rm :\longmapsto\: \sqrt[3]{4\dfrac{17}{27} }$

$\rm \:  =  \: \sqrt[3]{\dfrac{27 \times 4 + 17}{27} }$

$\rm \:  =  \: \sqrt[3]{\dfrac{108 + 17}{27} }$

$\rm \:  =  \: \sqrt[3]{\dfrac{125}{27} }$

$\rm \:  =  \: \dfrac{ \sqrt[3]{125} }{ \sqrt[3]{27} }$

Now, to find the cube roots, we use the concept of Method of Prime factorization.

$\purple{\rm :\longmapsto\:Prime \: factorization \: of \: 125}$

$\purple{\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{5}}}&{\underline{\sf{\:\:125\:\:\:}}}\\ {\underline{\sf{5}}}& \underline{\sf{\:\:25\:\:\:}} \\\underline{\sf{5}}&\underline{\sf{\:\:5\: \:\:}} \\ \underline{\sf{}}&{\sf{\:\:1\:\:\:}} \end{array}\end{gathered}\end{gathered}\end{gathered}}$

$\purple{\rm :\longmapsto\:Prime \: factorization \: of \: 125 = 5 \times 5 \times 5}$

$\red{\rm :\longmapsto\:Prime \: factorization \: of \: 27 }$

$\purple{\begin{gathered}\begin{gathered}\begin{gathered} \:\: \begin{array}{c|c} {\underline{\sf{3}}}&{\underline{\sf{\:\:27\:\:\:}}}\\ {\underline{\sf{3}}}& \underline{\sf{\:\:9\:\:\:}} \\\underline{\sf{3}}&\underline{\sf{\:\:3\: \:\:}} \\ \underline{\sf{}}&{\sf{\:\:1\:\:\:}} \end{array}\end{gathered}\end{gathered}\end{gathered}}$

$\red{\rm :\longmapsto\:Prime \: factorization \: of \: 27 = 3 \times 3 \times 3 }$

Hence, on substituting the values in above expression is

$\rm \:  =  \: \dfrac{ \sqrt[3]{5 \times 5 \times 5} }{ \sqrt[3]{3 \times 3 \times 3} }$

$\rm \:  =  \: \dfrac{5}{3}$

Hence,

$\rm\implies \:\boxed{\tt{ \: \: \sqrt[3]{4\dfrac{17}{27} } \: = \: \frac{5}{3} \: \: }}$

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MORE TO KNOW

$\begin{gathered}\boxed{\begin{array}{c|c} \bf x & \bf \sqrt[3]{x} \\ \frac{\qquad \qquad}{} & \frac{\qquad \qquad}{} \\ \sf 1 & \sf 1 \\ \\ \sf 8 & \sf 2 \\ \\ \sf 27 & \sf 3\\ \\ \sf 64 & \sf 4 \\ \\ \sf 125 & \sf 5\\ \\ \sf 216 & \sf 6 \\ \\ \sf 343 & \sf 7\\ \\ \sf 512 & \sf 8 \\ \\ \sf 729 & \sf 9 \end{array}} \\ \end{gathered}$