I HAVE A DOUT HOW CAN WE WRITE CUBE ROOT 2 IN NUMERICAL FORM
I HAVE A DOUT HOW CAN WE WRITE CUBE ROOT 2 IN NUMERICAL FORM
Here, the method to find the cube root of 113.
1. Draw a cube root symbol, or radical, with the number whose root you are seeking underneath. Start with the decimal point and mark off digits in both directions in groups of three. Put a decimal point above the radical, and directly above the other decimal point.
.
3/-----------
/ 113.000 000
2. Start with the first group of 1, 2, or 3 digits. Find the largest
cube of a single-digit integer less than it. Write the single digit above the radical, and its cube under the first group. Draw a line under that cube, and subtract it from the first group.
4.
3/-----------
/ 113.000 000
64
-------
49
3. Bring down the next group below the last line drawn. This forms
the current remainder. Draw a vertical line to the left of the
resulting number, and to the left of that line put three hundred times the square of the number above the radical, a plus sign, thirty times the number above the radical, a multiplication sign, an underscore character, another plus sign, another underscore character, the exponent 2, an equals sign, and some blank space for the answer.
4.
3/-----------
/ 113.000 000
64
-------
4800+120·__+__²=???? | 49 000
4. Pick the biggest digit D that would fit into both underscore
places, and give a number such that D times it is less than the current remainder. Put it above the radical above the last group of digits brought down, and put it in each of the blanks where the underscore characters are. Compute the number given by the expression, and put it after the equals sign. Multiply D times that number, and put that below the current remainder, draw a horizontal line below that, and subtract, to give a new current remainder.
4. 8
3/-----------
/ 113.000 000
64
-------
4800+120·8+8²=5824 | 49 000
46 592
----------
2 408
5. If the current answer, above the radical, has the desired accuracy, stop. Otherwise, go back to step 3.
Step 3:
4. 8
3/-----------
/ 113.000 000
64
-------
4800+120·8+8²=5824 | 49 000
46 592
----------
691200+1440·__+__²=?????? | 2 408 000
Step 4:
4 . 8 3
3/-----------
/ 113.000 000
64
-------
4800+120·8+8²=5824 | 49 000
46 592
----------
691200+1440·3+3²=695529 | 2 408 000
2 086 587
---------
321 413
Step 5: Stop.
Thus the cube root of 113 to two decimal places is 4.83. Checking,
4.83³ = 112.6786, and 4.84³ = 113.3799
Here, the method to find the cube root of 113.
1. Draw a cube root symbol, or radical, with the number whose root you are seeking underneath. Start with the decimal point and mark off digits in both directions in groups of three. Put a decimal point above the radical, and directly above the other decimal point.
.
3/-----------
/ 113.000 000
2. Start with the first group of 1, 2, or 3 digits. Find the largest
cube of a single-digit integer less than it. Write the single digit above the radical, and its cube under the first group. Draw a line under that cube, and subtract it from the first group.
4.
3/-----------
/ 113.000 000
64
-------
49
3. Bring down the next group below the last line drawn. This forms
the current remainder. Draw a vertical line to the left of the
resulting number, and to the left of that line put three hundred times the square of the number above the radical, a plus sign, thirty times the number above the radical, a multiplication sign, an underscore character, another plus sign, another underscore character, the exponent 2, an equals sign, and some blank space for the answer.
4.
3/-----------
/ 113.000 000
64
-------
4800+120·__+__²=???? | 49 000
4. Pick the biggest digit D that would fit into both underscore
places, and give a number such that D times it is less than the current remainder. Put it above the radical above the last group of digits brought down, and put it in each of the blanks where the underscore characters are. Compute the number given by the expression, and put it after the equals sign. Multiply D times that number, and put that below the current remainder, draw a horizontal line below that, and subtract, to give a new current remainder.
4. 8
3/-----------
/ 113.000 000
64
-------
4800+120·8+8²=5824 | 49 000
46 592
----------
2 408
5. If the current answer, above the radical, has the desired accuracy, stop. Otherwise, go back to step 3.
Step 3:
4. 8
3/-----------
/ 113.000 000
64
-------
4800+120·8+8²=5824 | 49 000
46 592
----------
691200+1440·__+__²=?????? | 2 408 000
Step 4:
4 . 8 3
3/-----------
/ 113.000 000
64
-------
4800+120·8+8²=5824 | 49 000
46 592
----------
691200+1440·3+3²=695529 | 2 408 000
2 086 587
---------
321 413
Step 5: Stop.
Thus the cube root of 113 to two decimal places is 4.83. Checking,
4.83³ = 112.6786, and 4.84³ = 113.3799
