Step calculation manual for square root

Calculation of the square root step by step When the square root of a number is calculated it is necessary to realize that the result cannot be a natural number, but a decimal number.

To calculate the square root of a number with several decimal digits we proceed this way: The number is divided into groups of two numbers, starting from the right. We will write it this way: We will write it: We write it in this way: It will be written as follows: When we do the subtraction it comes to zero and, therefore, it is not necessary to continue.

Written, this would be: We will write: We move down the following two digits. Welcome to our new "Getting Started" math solutions series. Over the next few weeks, we'll be showing how Symbolab Sign In. Sign in with Office Sign in with Facebook. Forgot Password Please enter your email address. An email notification with password reset instructions will be sent to you. Send Reset Link. We've sent the email to: [email protected]. Save Article. Like Article. Last Updated : 05 Oct, Recommended Articles.

Article Contributed By :. Easy Normal Medium Hard Expert. Writing code in comment? Please use ide. Load Comments. What's New. Most popular in Maths MAQ. What is the importance of the number system? In how many ways a committee consisting of 5 men and 3 women, can be chosen from 9 men and 12 women? What are the total possible outcomes when two dice are thrown simultaneously?

What are the different properties of trapezium? Which term of the progression 4, 9, 14, 19 is ? Most visited in School Learning. We use cookies to ensure you have the best browsing experience on our website. Start Your Coding Journey Now! We have several 2's in our square root. Since 2 is a prime number, we can remove a pair and put one outside the square root. From here, we can estimate Sqrt 2 and Sqrt 11 and find an approximate answer if we wish.

Method 2. Using a Long Division Algorithm. Separate your number's digits into pairs. This method uses a process similar to long division to find an exact square root digit-by-digit. Though it's not essential, you may find that it's easiest to perform this process if you visually organize your workspace and your number into workable chunks.

First, draw a vertical line separating your work area into two sections, then draw a shorter horizontal line near the top of the right section to divide the right section into a small upper section and a larger lower section. Next, separate your number's digits into pairs, starting from the decimal point. For instance, following this rule, 79,,, Write your number at the top of the left space. As an example, let's try calculating the square root of Draw two lines to divide your workspace as above and write "7 It's O.

You will write your answer the square root of Find the largest integer n whose square is lesser than or equal to the leftmost number or pair. Start with the leftmost "chunk" of your number, whether this is a pair or a single number. Find the largest perfect square that's less than or equal to this chunk, then take the square root of this perfect square.

This number is n. Write n in the top right space and write the square of n in the bottom right quadrant. In our example, the leftmost "chunk" is the number 7. Write 2 in the top right quadrant. This is the first digit of our answer. Write 4 the square of 2 in the bottom right quadrant. This number will be important in the next step. Subtract the number you just calculated from the leftmost pair.

As with long division, the next step is to subtract the square we just found from the chunk we just analyzed. Write this number underneath the first chunk and subtract, writing your answer underneath.

In our example, we would write 4 below 7, then subtract. This gives us an answer of 3. Drop down the next pair. Move the next "chunk" in the number whose square root you're solving for down next to the subtracted value you just found. Next multiply the number in the top right quadrant by two and write it in the bottom right quadrant.

In our example, the next pair in our number is "80". Write "80" next to the 3 in the left quadrant. Next, multiply the number in the top right by two.

Fill in the blank spaces in the right quadrant. You must fill each blank space you've just written in the right quadrant with the same integer. This integer must be the largest integer that allows the result of the multiplication problem in the right quadrant to be lower than or equal to the current number on the left.

This is greater than Therefore, 8 is too big, but 7 will probably work. Write 7 in the top right quadrant. This is the second digit in the square root of Subtract the number you just calculated from the current number on the left. Continue with the long-division style chain of subtraction. Take the result of the multiplication problem in the right quadrant and subtract it from the current number on the left, writing your answer below. In our example, we would subtract from , which gives us Repeat step 4.

Drop the next chunk of the number you're finding the square root of down. When you reach the decimal point in your number, write a decimal point in your answer in the top right quadrant.

In our example, since we are now encountering the decimal point in Next, drop the next pair 14 down in the left quadrant. Repeat step 5 and 6. Find the biggest digit to fill in the blanks on the right that gives an answer lesser than or equal to the current number on the left.

Then, solve the problem.