The technique to discover the square root of any kind of number is easy, if the given number is a perfect square. We can determine the square root of perfect squares by element factorisation method. However if the number is no a perfect square, climate it is challenging to uncover the square source of it. Hence, us then usage long department method.

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For example, the square source of 16 is 4, since 16 is a perfect square the 4, together as:

42 = 16 and √16 = 4. However the square root of 3, √3, is not easy, together 3 is no a perfect square.

Let united state learn here how to find the square source of number which are perfect and imperfect squares.

Finding Square root By element factorisation Method

We can always find the square root of perfect numbers making use of the element factorisation method. Let us see some examples here:

Square root of 81

Answer: By prime factorisation, us know:

81 = 3 x 3 x 3 x 3

Pairing the number to acquire the perfect squares we get;

81 = 9 x 9 = 92

Hence, √81 = 9

Find the square source of 625.

Answer: By element factorisation, us know:

625 = 5 x 5 x 5 x 5

Pairing the number to gain the perfect squares us get;

625 = 25 x 25 = 252

Hence, √625 = 25

How to uncover square root utilizing long department method

Another an approach to discover the square root of any kind of numbers is long department method. Let us see some instances here:

Example 1: uncover square source of 7921

The long department method because that √7921 have the right to be found as given below:


Hence, √7921 = 89

Since, 7921 is a perfect square, therefore, us can additionally find making use of factorisation method.

7921 = 89 x 89

Example 2: now if we have to discover the square root of 2, climate it is daunting to uncover using factorisation method. Hence, we deserve to determine √2 making use of long division method, as provided below:


We have the right to proceed additional to much more decimal places. Right here we have acquired √2 value upto 4 places the decimals.

Hence √2 = 1.4142..

Example 3: discover square root of 5 utilizing long division method.


Below room the steps described to uncover √5:

Write number 5 together 5.00000000Take the number who square is less than 5. Hence, 22 = 4 and also 4Divide 5 by together that when 2 multiplied by 2 provides 4. Subtract 4 native 5, friend will acquire the prize 1.Take two 0 in addition to 1 and take the decimal point after 1 in the quotient.Now add 2 in the divisor to do it 4. Take it a number beside 4, such that once we multiply through the very same as a whole, climate it results in the value much less than or equal to 100. Hence, 42 x 2 = 84 is much less than 100.Now write it listed below 100 and subtract that from 100 to get the remainder.Next remainder is 16Again bring down two pairs that zero and also repeat step 5 as much as 4 places of decimals.Finally, you acquire the answer as 2.2360…You can repeat the technique further.

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Square root of Decimal Number

The decimal numbers could be a perfect square or not. But, to discover its square root we cannot use factorisation technique directly. Let united state see an example:

Example: √6.25 =?

Let united state write 6.25 as 625/100

Now we know:

625 = 25 x 25

100 = 10 x 10

√625 = 25 and also √100 = 10

Thus, √6.25 = √(625/100) = 25/10 = 2.5

Hence, we discovered the square root of 6.25 equal to 2.5.

Now, if we have actually to discover square root of a decimal number making use of long department method, then see the example given below: