Calculate Square Root . . . without using a square root calculator Show Return To "Top of Page" click here Example of Direct
Calculation Calculate Square Root: Step 1: Beginning at the decimal point, divide the radicand into groups of two digits in both directions. The decimal can be extended as far as you wish.
Step 2: Beginning on the left, select the first group of one or two digits. In this example , the first group of digits in the radicand is simply the number 2 .
Step 3: If possible, find the perfect square root (expressed as an integer) of the first group of digits in the radicand. Or, If the first group of digits does not have a perfect square root (expressed as an integer), find the perfect square root of the number closest to, but less than, the first group of digits. In this example , the number 2 does not have a perfect square root (which can be expressed as an integer). The number closest to, but less than, the number 2 which has a perfect square root is the number 1 . The perfect square root of the number 1 is also 1 . Write this number above the radical sign as shown below.
Step 4: Square the answer to step 3, and subtract it from the first group of numbers. In this example , the number 1 squared is subtracted from the number 2 .
Step 5:
In this example, bring down 73.
In this example, the number 1 x 2 = 2.
In this example, the new digit is 6. The resulting number (26), can be divided into 173 a total of 6 times.
Step 6: Repeat steps A, B, and C shown in step 5.
In this example, bring down 00.
In this example, the number 16 x 2 = 32.
In this example, the new digit is 5. The resulting number (325), can be divided into 1700 a total of 5 times.
Step 7: Repeat steps A, B, and C shown in step 5.
In this example, bring down 00.
In this example, the number 165 x 2 = 330.
In this example, the new digit is 2. The resulting number (3302), can be divided into 7500 a total of 2 times.
Step 8: Repeat steps A, B, and C shown in step 5.
In this example, bring down 00.
In this example, the number 1652 x 2 = 3304.
In this example, the new digit is 2. The resulting number (33042), can be divided into 89600 a total of 2 times.
The final answer is:
to 3 decimal points (not rounded) Cube Roots: calculating cube roots by hand is more complicated than computing square roots by hand. For information on cube roots, see the following web sites: http://mathforum.org/library/drmath/view/52605.html http://www.mathpath.org/Algor/cuberoot/algor.cube.root.htm Example of Newton's Method The three steps used to Calculate Square Roots are:
Video demonstrating this method - click here Calculate Square Root: 1st Approximation: Calculate Square Root - Newton's Method
In this example, a good initial estimate for the square root of 273 is 15 . (However, the initial estimate could be "any" number. Subsequent steps will refine the estimate.)
In this example, divide 273 by 15.
In this example, , find the average of 15 and 18.2 .
1st Approximation of Square Root is: 2nd approximation:
In this example, the initial estimate will be 16.6
In this example, divide 273 by 16.6 .
In this example, , find the average of 16.6 and 16.445783 .
2nd Approximation of Square Root is: 3rd approximation:
In this example, the initial estimate will be 16.522892
In this example, divide 273 by 16.522892 .
In this example, , find the average of 16.522892 and 16.522531 .
3rd Approximation of Square Root is: (Final answer for this example)
Example of the Guess & Check Method The four steps used to Calculate Square Roots are:
Calculate Square Root: 1st Approximation: Calculate Square Root - Guess & Check Method
In this example, , a good initial estimate for the square root of 273 is 15 (However, the initial estimate could be "any" number.)
In this example , multiply 15 by 15 .
In this example, 225 is less than 273.
In this example, since 225 is less than 273 the estimate will be increased from 15 to 16 . Refined estimate of Square Root is: 2nd Approximation: Calculate Square Root - Guess & Check Method
In this example , the estimate for the square root of 273 has been raised to 16
In this example , multiply 16 by 16.
In this example, 256 is still less than 273.
In this example , since 256 is less than 273 (but closer than the original estimate) the estimate will be increased a small amount, from 16 to 16.5 . Refined estimate of Square Root is: 3rd Approximation: Calculate Square Root - Guess & Check Method
In this example , the estimate for the square root of 273 has been raised to 16.5
In this example , multiply 16.5 by 16.5
In this example, 272.25 is still less than 273 , but it is much closer than the other estimates.
In this example , since 272.25 is less than 273 (but much closer than the other two estimates) the estimate should be increased slightly . Refined estimate of Square Root so far is: How do you find the square root without the button?To find the square root of a whole number, you could also divide the whole number by numbers until you get an answer that is the same as the number you used to divide the whole number. For example: 16 divided by 4 is 4. And 4 divided by 2 is 2, and so on.
How do you manually calculate square roots?Long division method. Separate your square root base into pairs. ... . Find the largest square that divides into the first number or pair. ... . Subtract the square from the first number or pair. ... . Drop down the next pair. ... . Multiply the first digit of the square by two. ... . Set up the next factor equation.. Is there a shortcut for square root?Finally, you can use a shortcut combination to insert the square root key. On your keyboard, press Alt, 2, 5 and then 1.
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