Answer

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Hint: First of all let 2744 = a. To find the cube root of 2744, first of all factorize it and then find the cube root that is \[{{a}^{\dfrac{1}{3}}}\] or \[{{\left( 2744 \right)}^{\dfrac{1}{3}}}\].

Complete step-by-step answer:

Here, we have to find the cube root of 2744.

Before proceeding with this question, we must know what a cube root is.

Cube root of a number is a special value that, when used in a multiplication three times, gives that number. In other words, we can say that the cube root of a number ‘x’ is a number ‘y’ such that \[y\times y\times y=x\] or \[{{y}^{3}}=x\]. Therefore, we get the cube root of x, that is \[y={{x}^{\dfrac{1}{3}}}\].

The graph for \[y={{x}^{\dfrac{1}{3}}}\] can be drawn as

This plot is symmetric with respect to the origin.

Now, here we have to find the cube root of 2744.

Let us take a = 2744.

Therefore, we get the cube root of 2744 as,

\[{{a}^{\dfrac{1}{3}}}={{\left( 2744 \right)}^{\dfrac{1}{3}}}....\left( i \right)\]

First of all, we will resolve 2744 into its factors as follows. Now, we will use the method of factorization, that is,

Therefore, we get \[2744=2\times 2\times 2\times 7\times 7\times 7\]

We can also write it as, \[2744={{2}^{3}}{{.7}^{3}}\].

By putting the value of 2744 in equation (i), we get

\[{{a}^{\dfrac{1}{3}}}={{\left( {{2}^{3}}{{.7}^{3}} \right)}^{\dfrac{1}{3}}}\]

We know that \[{{a}^{n}}.{{b}^{n}}={{\left( ab \right)}^{n}}\].

By applying this in the above equation, we get,

\[{{a}^{\dfrac{1}{3}}}={{\left( {{14}^{3}} \right)}^{\dfrac{1}{3}}}\]

We know that \[{{\left( {{a}^{n}} \right)}^{m}}={{a}^{nm}}\]. By applying this in the above equation, we get,

\[{{a}^{\dfrac{1}{3}}}={{\left( 14 \right)}^{3\times \dfrac{1}{3}}}\]

Therefore, we get \[{{a}^{\dfrac{1}{3}}}=14\]

Hence, we have found that the cube root of 2744 is 14.

Note: Students should properly factorize the given number and cross-check if they are getting the same number by multiplication of factors or not. Also, after finding the cube root, students can take a cube of that cube root to find if it is giving the correct number or not. Students can cross-check in this way.

As we have found that the cube root of 2744 is 14.

We will find \[{{14}^{3}}=14\times 14\times 14\]

We get, \[{{14}^{3}}=2744\]

Therefore, our answer is correct.

Complete step-by-step answer:

Here, we have to find the cube root of 2744.

Before proceeding with this question, we must know what a cube root is.

Cube root of a number is a special value that, when used in a multiplication three times, gives that number. In other words, we can say that the cube root of a number ‘x’ is a number ‘y’ such that \[y\times y\times y=x\] or \[{{y}^{3}}=x\]. Therefore, we get the cube root of x, that is \[y={{x}^{\dfrac{1}{3}}}\].

The graph for \[y={{x}^{\dfrac{1}{3}}}\] can be drawn as

This plot is symmetric with respect to the origin.

Now, here we have to find the cube root of 2744.

Let us take a = 2744.

Therefore, we get the cube root of 2744 as,

\[{{a}^{\dfrac{1}{3}}}={{\left( 2744 \right)}^{\dfrac{1}{3}}}....\left( i \right)\]

First of all, we will resolve 2744 into its factors as follows. Now, we will use the method of factorization, that is,

Therefore, we get \[2744=2\times 2\times 2\times 7\times 7\times 7\]

We can also write it as, \[2744={{2}^{3}}{{.7}^{3}}\].

By putting the value of 2744 in equation (i), we get

\[{{a}^{\dfrac{1}{3}}}={{\left( {{2}^{3}}{{.7}^{3}} \right)}^{\dfrac{1}{3}}}\]

We know that \[{{a}^{n}}.{{b}^{n}}={{\left( ab \right)}^{n}}\].

By applying this in the above equation, we get,

\[{{a}^{\dfrac{1}{3}}}={{\left( {{14}^{3}} \right)}^{\dfrac{1}{3}}}\]

We know that \[{{\left( {{a}^{n}} \right)}^{m}}={{a}^{nm}}\]. By applying this in the above equation, we get,

\[{{a}^{\dfrac{1}{3}}}={{\left( 14 \right)}^{3\times \dfrac{1}{3}}}\]

Therefore, we get \[{{a}^{\dfrac{1}{3}}}=14\]

Hence, we have found that the cube root of 2744 is 14.

Note: Students should properly factorize the given number and cross-check if they are getting the same number by multiplication of factors or not. Also, after finding the cube root, students can take a cube of that cube root to find if it is giving the correct number or not. Students can cross-check in this way.

As we have found that the cube root of 2744 is 14.

We will find \[{{14}^{3}}=14\times 14\times 14\]

We get, \[{{14}^{3}}=2744\]

Therefore, our answer is correct.

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