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How to Find Square Root Without Calculator

To find the square root of a number without a calculator, you can use the long division method. Begin by making two columns on paper and label them quotient and remainder. Put the number for which you’d like to calculate the square root in the remainder column.

Then divide that number by your best guess as to what its square root is and place that value in the quotient column. Multiply this value by itself to check if it matches your original number, or if it’s too large or too small. If it’s not quite right, adjust your initial guess up or down accordingly until you arrive at an answer that matches exactly with what was initially placed in the remainder column.

  • Step 1: Start by writing down the number whose square root you want to find
  • Step 2: Divide the number into two parts such that one part contains an even number of digits and other part contains an odd number of digits
  • For example, if the given number is 8356 then divide it into 83 and 56
  • Step 3: Find the largest perfect square that can be formed from the first half (83 in our case) using prime factorization
  • In this case, 81 is a perfect square so we can take its root as 9
  • This will be our starting point for finding out the actual square root of 8356
  • Step 4: Now start subtracting successive odd numbers from 81 (starting with 1) until we get a result which is less than or equal to 56 (second half)
  • The last odd number subtracted will give us our answer’s second digit after decimal place i
  • , 7 in this case since 81-1 = 80 56
  • Step 5 : Repeat step 4 with each successive pair of digits starting from right side till all digits are exhausted which would give us complete answer i
How to Find Square Root Without Calculator


How Do You Find the Square Root of a Number Without a Calculator?

Finding the square root of a number without a calculator is an important math skill to have. One of the most efficient and accurate ways to find the square root of a number is by using long division. To use this method, you will need to break down your number into two-digit numbers in order for it to be properly divided.

Once you divide your number, you can then begin subtracting from it until there are no more digits left or until you reach 0. After that, multiply each pair of digits together and add them together at the end for your answer! Another way would be using estimation methods such as finding patterns between squares such as 3² = 9 so 4² = 16 which means 5² must be 25.

This method requires practice but can become quite useful if used correctly! Finally, one last way would be factoring out perfect squares from our original number and then taking the square root of those perfect squares in order to obtain our final answer. For instance 12 = 2*2*3 so its square root must equal √2 *√2 *√3 which equals 2 *1 * 1 .5 which all adds up to 3!

How Do You Manually Find Square Root?

Finding the square root of a number can be done manually with some simple steps. To start, you’ll need to determine if the number is a perfect square or not. If it is, then you can use the quick and easy method of multiplying one-half by itself until you get your desired result (e.g., 4 x 4 = 16; 1/2 x 1/2 = 1/4).

For numbers that are not perfect squares, however, there is another way: the long division method. This involves dividing your large number into two smaller equal parts and then finding their product. For example, if we wanted to find the square root of 81, we would divide it into 9 and 9 since they both add up to 81 (9 x 9 = 81).

Once this has been completed, simply multiply these two factors together and voila! You have your answer – in this case it’s 3×3=9 which confirms that √81=9!

What is the Easiest Way to Find the Square Root of Anything?

Finding the square root of a number can seem daunting, but there are actually quite a few easy ways to do it. One of the simplest is by using a calculator; most calculators have an option for calculating square roots, making it as easy as entering your number and pressing the button. Another way to find the square root is to use long division.

This method involves dividing your chosen number repeatedly until you get close enough that you can estimate its square root with reasonable accuracy. A third option is factorization; this involves arranging the given number into pairs of factors that add up to itself, then finding their respective roots in order to determine what two numbers multiplied together will equal your original one. Finally, if all else fails, you can always look up tables or online resources which list exact values for different square roots so you don’t have to go through any calculations yourself!

How Do I Figure Out the Square Root of a Number?

Figuring out the square root of a number can be quite daunting, especially if you don’t have any prior knowledge or experience in mathematics. Fortunately, there are various methods that you can use to calculate the square root of a number without having to rely on memorizing long equations or formulas. The most common method is using an online calculator which can quickly provide accurate results.

You can also use the factorization method where you divide your number into factors and then take out all pairs of identical factors – this will give you the square root. If your number is not divisible by any factors, then try using a chart – these charts list common numbers and their corresponding square roots so it’s easy to determine what your answer should be. Another great way for determining the square root of larger numbers is by estimating with perfect squares – knowing some basic squares (4 = 2², 9 = 3² etc) can help narrow down what your answer could possibly be before making more specific calculations.

Lastly, if all else fails and none of these methods seem applicable to what you’re trying to do, why not consult an expert? A math tutor or teacher may be able to offer advice on how best to proceed with figuring out the correct answer when calculating complex problems such as this one!

Find Square Root by Hand without Calculator

How to Find Square Root Manually

Manually finding the square root of a number can be done using the long division method. To start, divide the number you are trying to find the square root of by a single-digit divisor that is less than or equal to its last digit. Then use trial and error as you work through each remainder until you have an answer with no remainder.

This requires patience and practice but gives satisfactory results once mastered!

How to Find Square Root Easily

Finding the square root of a number can be done quickly and easily with an online calculator or by simply using long division. For numbers that have perfect squares, such as 4, 9, 16 and 25, you can use a multiplication table to arrive at their square roots – 2 for 4; 3 for 9; 4 for 16; and 5 for 25. Otherwise, long division is the best way to find the square root of any number.

How to Find Square Root With Calculator

Using a calculator to find the square root of a number is quick and easy. All you need to do is enter the desired number into your calculator and hit the “square root” button, usually indicated by an √ symbol. The result will be displayed on your screen in seconds!

If you’re using an older model of calculator that doesn’t have this feature, don’t worry – simply type in the number multiplied by itself (the same as squaring it) then press the “equals” button to get your answer.

How to Calculate Square Root by Division Method

The Division Method is a reliable way to calculate the square root of any number. To use this method, you will need to divide the given number by one more than its largest possible divisor and then continue dividing until you reach an answer that has no remainder. This process requires patience and accuracy; however, it can be used to find approximate values for square roots of large numbers if necessary.


In conclusion, finding the square root of a number can be done without the use of a calculator. Through practice and memorization of perfect squares, you can gain skills to help you find approximate solutions quickly. Additionally, there are multiple methods that allow for greater accuracy when finding square roots such as prime factorization or using long division.

With these various tools in your arsenal, you should be able to tackle any problem involving square roots with confidence!