Square Root of 30

As per mathematical historian D.E. Smith, Aryabhata's method for finding out the square root was introduced in Europe by Cataneo in 1546. The symbol of square root was first used by Christoph Rudolf in 1525 to represent taking square root. If we talk about square root of certain natural numbers, we would end up with a conclusion that some of them are rational numbers an some are irrational numbers. In another words some are perfect squares some are not. Let us talk about number 30. 30 is not a perfect square; hence its square root is irrational number. This concludes that square root of any number "n" which is not a perfect square will always be an irrational number. Let us have answer to the questions like what is the square root of 30, how to find the square root of 30 alsong with some tips and tricks.

• Square Root of 30: √30 = 5.477
• Square of 30: 30² = 900 

Square root of 30 is the value which is obtained after taking square root of 30. Do you think 30 can be broken into two parts such that each part on multiplication gives a value 30? Let's have a look at factors of 30.
We can see that each number which is a factor of 30 does not result in 30 on squaring. That gives us the answer that 30 cannot be broken into two parts such that each part on multiplication gives a value 30. Hence, when square root of 30 is taken, following value is obtained.

It is not possible to dissociate 30 into two such factors which on multiplying give 30. 30 can be approximately written as a square of 5.477, which is a non-recurring and non-terminating decimal number.This shows it isn't a perfect square, which also proves that the square root of 30 is an irrational number.

Square root of 30 is found using the following steps:

Step 1: Check whether the number is perfect square or not. 30 is not a perfect square as it cannot be broken down into a product of two same numbers.
Step 2: Once the number is checked, following is the processes required to be followed:

• If the number is a perfect square, it can be written in this format: √x² = x. If the number is not a perfect square, the square root is found using the long division method.
• It can also be written in its simplified radical form of square root.
• In this case, 30 is not a perfect square; hence its square root is found using the long division method. The simplified radical form of square root of 30 is given as below.

Simplified Radical Form of Square Root of 30

• 30 can be written as a product 5 and 6
• But neither is 5 a perfect square, nor is 6 a perfect square.
• Hence, it is given as √30
• 30 is not a perfect square; hence it remains within roots.
• Simplified radical form of square root of 30 is √30

Square Root of 30 By Long Division

Let us understand the process of finding square root of 30 by long division.

• Step 1: Pair the digits of the number from one's digit. 30 has 2 digits. Digits are paired from right side. We show the pair by placing a bar over them.
• Step 2: Now we find a number such that the square of the number gives product less than or equal to the first pair. Here, the pair just consists of 30. Square of 5 gives product less than 30. On subtracting 30 from square of 5, we get 5.
• Step 3: Now we take the double of quotient and place a digit with divisor along with its placement in quotient, such that the new divisor when multiplied with the individual number in quotient gives the product less than the dividend subsequently subtracting it from the dividend. A pair of zeros are added after decimal. The double of 5 gives 10 and a digit is written such that the product of the three digit number with the quotient gives product less than 500. Now a decimal is added to the quotient, hence letting us add a pair of zeros to the original dividend.
• The new 3-digit divisor is now 104 and that on multiplication to 4 gives 416. On subtracting 416 from 500 we get 84
• Step 4: For the new dividend obtained, we take the double of quotient and place a digit with divisor along with its placement in quotient, such that the new divisor when multiplied with the individual number in quotient gives the product less than the dividend. The double of quotient gives 108 and a pair of 0's is added to the dividend. The fourth digit of the divisor is found such that the product of it with the quotient a value lesser than the dividend.
• Step 5: The difference is obtained in the above step. The double of quotient is again taken and used as a divisor along with the involvement of one more digit such that the same digit is mentioned in the quotient, resulting in a product less than the new divisor. The digit that is written in blank space is 7. The product of 1087 to 7 gives 7606 which is less than 8400. On the subtraction of 7609 from 8400, we get 791 with a new pair of zeros in the dividend. The quotient is again doubled, which gives the value 1094
• Step 6: The process is repeated. Hence, the division is shown as:

Explore Square roots using illustrations and interactive examples

• Square Root of 28
• Square Root of 34
• Square Root of 35
• Square Root of 36
• Square Root of 29

• How will Hailey find the square root of 30 using long division method upto 7 decimal places?
• How will Billy express the square root of 300 in terms of square root of 30?