how to find the square root of a big number without a calculator Athenian Stranger 10 4K subscribers 21K 1 2M views 4 years ago squareroots byhand withoutcalculator Learn how to find the square root of a number by hand approximated to at least two
Try it 2 2 4 and 2 2 4 Since a square root of a number must equal that number when multiplied by itself When you multiply this number by itself and set it up as a full equation n n x the two factors n and n are either both positive or both negative since they are the same number Let us find out the trick to determine the root of large numbers Example 1 Suppose we need to find the square root of large numbers such as 4489 Step 1 The unit digit in this number is 9 which can be a unit digit of its square root number such as 3 or 7 Because 3 2 is 9 and 7 2 is 49
how to find the square root of a big number without a calculator
how to find the square root of a big number without a calculator
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By prime factorisation we get 400 2 x 2 x 2 x 2 x 5 x 5 Now pairing the common numbers in a pair of two we see here three pairs Two pairs of 2 and one pair of 5 Therefore 400 2 x 2 x 2 x 2 x 5 x 5 Taking out the numbers in pairs 400 2 x 2 x 5 20 Hence the square root of 400 is 20 Solution 484 2 2 11 11 So 484 2 2 11 11 2 11 22 Guess Check method This method is used to give the approximate value of any number The guess method saves time as it gives an approximate range of values between which the root exists it is more efficient when the number inside the root is an imperfect number
20 10 20 10 since 20 2 20 10 2 10 20 2 20 10 2 10 To calculate by hand a square root there is an algorithm similar to the division algorithm that I learnt in grade 6 Here is how it goes for the square root of 20 20 Now divide your number by one of the perfect square roots you found For example you would divide 7 by either 2 or 3 If you were to choose 3 your answer would be 2 33 Next find the average of that number and the perfect square root To find the average in this example add 2 33 and 2 then divide by 2 and get 2 16
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Embark on a comprehensive step by step guide to finding square roots without a calculator Follow each instruction closely and witness the magic of mental math unfold Practice Exercises Subtract the product we calculated which is 425 from the current number on the left also 425 The result is zero which means the task is complete Note I chose a perfect square 2025 45 x 45 on purpose This way I could show the rules for solving square root problems
The Organic Chemistry Tutor 7 71M subscribers 970K views 4 years ago New Algebra Playlist more This math video tutorial explains how to find the square root of a large number 2 Answers Sorted by 1 Here is a good page to learn basic mathematics square root algorithm html Also Newton made a great approximation So pick an approximate square root A A In this case it would be 6 6 since 35 35 is close to 36 36 Then calculate 1 2 N A A 1 2 N A A Where N N is the number 35 35
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how to find the square root of a big number without a calculator - Solution 484 2 2 11 11 So 484 2 2 11 11 2 11 22 Guess Check method This method is used to give the approximate value of any number The guess method saves time as it gives an approximate range of values between which the root exists it is more efficient when the number inside the root is an imperfect number