Question

Solve the following.
3×cbrt(11​

Answer 1

Answer:

Now, let us figure out the value of 3√3, step by step.

Let us assume the cube root of 3 is equal to x.

Then, x = 3√3

As we know,

13 = 1 and 23 = 8

Hence, x lies between 1 and 8. But, it lies closer to number 1 than 8, if we see in a number line. Hence, we can assume a value, say 1.4, which could be approx to the cube root of 3.

Now to determine the value of 3√3, we need to divide 3 by the estimated value.

Divide 3 by 1.4.

3/1.4 = 2.1428

Again, divide this value by 1.4.

2.1428/1.4 = 1.53

Now, take the average of 1.4, 1.4 and 1.53 to get a value of 3√3.

(1.4+1.4+1.53)/3 = 1.44

The actual value of 3√3 is 1.442249.

Hence, 1.44 is approximately equal to 1.442249.

Cube Root Lists

Below is the table for the cube root of numbers from 1 to 25.

Number

Cube root ∛a

1

1.000

2

1.260

3

1.442

4

1.587

5

1.710

6

1.817

7

1.913

8

2.000

9

2.080

10

2.154

11

2.224

12

2.289

13

2.351

14

2.410

15

2.466

Step-by-step explanation:

Now, let us figure out the value of 3√3, step by step.

Let us assume the cube root of 3 is equal to x.

Then, x = 3√3

As we know,

13 = 1 and 23 = 8

Hence, x lies between 1 and 8. But, it lies closer to number 1 than 8, if we see in a number line. Hence, we can assume a value, say 1.4, which could be approx to the cube root of 3.

Now to determine the value of 3√3, we need to divide 3 by the estimated value.

Divide 3 by 1.4.

3/1.4 = 2.1428

Again, divide this value by 1.4.

2.1428/1.4 = 1.53

Now, take the average of 1.4, 1.4 and 1.53 to get a value of 3√3.

(1.4+1.4+1.53)/3 = 1.44

The actual value of 3√3 is 1.442249.

Hence, 1.44 is approximately equal to 1.442249.

Cube Root Lists

Below is the table for the cube root of numbers from 1 to 25.

Number

Cube root ∛a

1

1.000

2

1.260

3

1.442

4

1.587

5

1.710

6

1.817

7

1.913

8

2.000

9

2.080

10

2.154

11

2.224

12

2.289

13

2.351

14

2.410

15

2.466