How To Quickly Find The Square Root Of A Number

How to find the square root of a number and calculate it by hand

At times, in everyday situations, we may face up the job of having to figure the foursquare root of a number. What if there is no calculator or a smartphone handy? Tin can we use an sometime fashioned newspaper and pencil to do it in a long division style?

Yep we tin, and there are several different methods. Some are more than circuitous than others. Some provide more accurate results.

The one I want to share with you is one of them. To make this commodity more than reader friendly, each stride comes with illustrations.

STEP one: Divide The Digits Into Pairs

To brainstorm, allow'south organize the workspace. We volition divide the infinite into three parts. Then, allow's split up the number'south digits into pairs moving from right to left.

For instance, the number seven,469.17 becomes 7469.17. Or in the instance of a number with an odd amount of digits such every bit nineteen,036, nosotros will start with 19036.

In our case here, 2,025 becomes xx25.

Step 2: Find The Largest Integer

Every bit the next step, we need to observe the largest integer (i) whose square is less than or equal to the leftmost number.

In our electric current example the leftmost number is 20. Since 4² = xvi <= xx and 5² = 25 > 20, the integer in question is 4. Let'due south deposit 4 to the top-right corner and iv² = 16 to the bottom right one.

Stride three: Now Subtract That Integer

Now we need to decrease the square of that integer (which equals 16) from the leftmost number (which equals xx). The outcome equals 4 and we volition write information technology every bit shown above.

STEP 4: Let's Move To The Next Pair

Adjacent, allow's move downwardly the next pair in our number (which is 25). We write it next to the subtracted value already there (which is 4).

Now multiply the number in the acme right corner (which is likewise 4) past 2. This results in 8 and nosotros write it in the lesser correct corner followed by_ x _ =

Footstep 5: Observe The Right Match

Time to make full in each blank space with the same integer (i). It must be the largest possible integer that allows the product to be less than or equal the number on the left.

For example, if we choose the number six, the first number becomes 86 (viii and 6) and we must too multiply it by half-dozen. The result 516 is greater than 425, so nosotros become lower and try five. The number eight and the number 5 give us 85. 85 times five results in 425, which is exactly what we need.

Write v next to 4 in the acme right corner. It is the second digit in the root.

STEP 6: Subtract Once more

Subtract the production we calculated (which is 425) from the current number on the left (also 425). The consequence is zero, which ways the task is consummate.

Note: I chose a perfect square (2025 = 45 x 45) on purpose. This way I could testify the rules for solving square root issues.

In reality, numbers consist of many digits, including the ones subsequently the decimal point. In that case we repeat steps four, five and 6 until we reach any accuracy we want.

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