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# How to find square roots without a calculator? – GeeksforGeeks

The total system is the organization defined for the different numbers and the way they could be arranged. There are many types of number systems but largely 4 types are well known. They are binary act systems, Decimal number systems, octal issue systems, and Hexadecimal number systems. The decimal number system is by and large used in mathematics, it involves numbers from 0-9. There are multiple operations done on the numbers, for example, finding squares and square roots of numbers, lets learn in detail about the square roots of the numbers ,

### Square root

The square root of a count is a value which when multiplied with itself gives the original count. For model, the square root of 9 is 3, when 3 is multiplied by itself, the original total obtained is 9. The symbol that denotes square root in mathematics is √. This symbol ( √ ) is called radical and the count inside the root symbol is known as radicand. The number or the value award inside the rout symbol might be a perfective square or an progressive square. For example- 4 is a perfect square whereas 3 is an progressive hearty. So, based on the nature of respect inside the ancestor, the final answer or the squarely root may be a natural issue of a decimal total.
now let ’ s find out how to calculate the square root of different numbers .

### Square roots without a calculator

As above defined, the square root of a act is the measure which when multiplied with itself will provide the original act only. There are three ways to find square root without a calculator

Prime factorization This is a long but simple method acting to find the square root of any number. Prime factorization involves finding factors of that total and then pairing the common numbers in a pair of two. finally, taking the straight roots of the prime factors. Let ’ s see an case of this, Question: find the square root of 484 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 prize of any number. The guess method saves prison term as it gives an approximate range of values between which the settle exists. it is more efficient when the phone number inside the root is an fallible number. Let ’ s see an example of this, Question: find the square root of 20. Solution:

Start guess and check method acting by noting that since √16 = 4 and √25 = 5, then √20 must be between 4 and 5. As second measure, in decree to reach near to the actual answer, lets take a numeral between 4 and 5. lets assume it to be 4.5. Lets do square of 4.5 which comes out to be 20.25, which is greater than 20, therefore the settle must be smaller than 4.5, lets choose 4.4, feather of 4.4 is 19.36. thus, the most approx and accurate root of 20 is 4.4

Long division method It is a very easy direction to get the square root of progressive squares. The long division method is by and large preferred over the early methods since it provides an accurate answer. Let ’ s understand this algorithm using an model, Question: find the square root of 627

Solution: Step 1 Group the numbers in pairs from right to left, leaving one or two digit in bequeath ( here its 6 ). Step 2 Think of a number whose square is less than the first number ( 6 ), its 2, so, write it like this – Step 3 Is to square the number 2 and write the result below 6 and then subtract as shown below, Step 4 Multiply the quotient by 3 and and write it down in parenthesis with an empty pipeline next to it as shown below, Step 5 now find out the number which when multiplied by forty something would be lesser than 225. Lets guess 5. then 45×5=225, which is less than 227, so write it as shown below- Step 6 then repeating pace 4, multiply the quotient with 2 write it down in digression with an empty lineage next to it as shown below, Step 7 Repeating step 5, find out the number which when multiplied by five hundred something would be lesser than 2000. Lets guess 5, then 505×5=2525, which is bigger than 2000, lets think 4, then 504×3=1512. so publish it as shown below, The square root of 627 with two decimal place is 25.03, which is accurate.

### Sample Problems

Question 1: Find the square root of 144 Solution:

144=2 × 2 × 2 × 2 × 3 × 3 so √144= √ ( 2 × 2 × 2 × 2 × 3 × 3 ) = 2 × 2 × 3 =12

Question 2: Find the square root of 169 Solution:

169=13 × 13 thus √144= √ ( 13 × 13 ) = 13

Question 3: Find the square root of 6 by the Guess and check method. Solution:

Start estimate and check the method by noting that since √9 =3 and √4 = 2, then √6 must be between 2 and 3. As the moment mistreat, in order to reach near to the actual answer, let ’ s take a count between 2 and 3. Let ’ s assume it to be 2.5. Let ’ s do a square of 2.5 which comes out to be 6.25, which is greater than 6. therefore the root must be smaller than 2.5. Let ’ s choose 2.4, square of 2.4 is 15.76. thus, the most approx and accurate root of 6 is 2.4

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