# Square root of a number without using calculator

Category : EDUCATION Author : Gopesh Shukla Date : Sun Jan 28 2018 Views : 62

This method comes handy when the square root of a number is to be found and one may not use a calculator or have it in possession. The method involves 3 simple steps and is often accurate up to the second decimal place. It involves basic arithmetic operations and can be really helpful especially, for young aspirants who have been preparing themselves for various competitive examinations. This is how it works.

Suppose the given number is **50**, square root of 50 is;

Well, let's find out.

*Step 1:* Choose a number whose square is close to the given number. (The closer the square, accurate the answer). There are multiple options *viz.* 6 whose square leads to 36, 7 whose square leads to 49 and 8 which yields 64. Closest to 50 is *49*, hence **7** is chosen.

**Step 2:** Divide the given number by the number chosen above. That is, divide *50* by *7* which yields approximately **7.14.**

*Step 3:* Take the average of the quotient obtained and the number chosen, that is, add *7.14* to *7* and divide the sum * **14.14* by *2*. The result obtained is **7.07** *which is the square root of 50 accurate up to 2 decimal places.*

*Step 4**:* Compare the results with a calculator.

Let's take another example suppose **110**, following the same steps:

*Step 1:* Choose a number whose square is close to the given number. (The closer the square, accurate the answer). There are multiple options *viz.* 10 whose square leads to 100, 11 whose square leads to 121 and 12 which yields 144. Closest to 110 is *100*, hence **10** is chosen.

*Step 2:* Divide the given number by the number chosen above. That is, divide *110* by *10* which yields approximately **11.0.**

**Step 3:** Take the average of the quotient obtained and the number chosen, that is, add *11.0* to *10* and divide the sum * 21.0* by *2*. The result obtained is **10.5** *which is the square root of 110.*

*Step 4**:* Compare the results with a calculator, which states the square root to be 10.48 which can be approximated to *10.5.*

Thanks for reading. Hope this helps!

This method comes handy when the square root of a number is to be found and one may not use a calculator or have it in possession. The method involves 3 simple steps and is often accurate up to the second decimal place. It involves basic arithmetic operations and can be really helpful especially, for young aspirants who have been preparing themselves for various competitive examinations. This is how it works.

Suppose the given number is **50**, square root of 50 is;

Well, let's find out.

*Step 1:* Choose a number whose square is close to the given number. (The closer the square, accurate the answer). There are multiple options *viz.* 6 whose square leads to 36, 7 whose square leads to 49 and 8 which yields 64. Closest to 50 is *49*, hence **7** is chosen.

**Step 2:** Divide the given number by the number chosen above. That is, divide *50* by *7* which yields approximately **7.14.**

*Step 3:* Take the average of the quotient obtained and the number chosen, that is, add *7.14* to *7* and divide the sum * **14.14* by *2*. The result obtained is **7.07** *which is the square root of 50 accurate up to 2 decimal places.*

*Step 4**:* Compare the results with a calculator.

Let's take another example suppose **110**, following the same steps:

*Step 1:* Choose a number whose square is close to the given number. (The closer the square, accurate the answer). There are multiple options *viz.* 10 whose square leads to 100, 11 whose square leads to 121 and 12 which yields 144. Closest to 110 is *100*, hence **10** is chosen.

*Step 2:* Divide the given number by the number chosen above. That is, divide *110* by *10* which yields approximately **11.0.**

**Step 3:** Take the average of the quotient obtained and the number chosen, that is, add *11.0* to *10* and divide the sum * 21.0* by *2*. The result obtained is **10.5** *which is the square root of 110.*

*Step 4**:* Compare the results with a calculator, which states the square root to be 10.48 which can be approximated to *10.5.*

Thanks for reading. Hope this helps!

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