Square Root of 67
67 is a prime number. When we determine the square root of any prime number n, the square root of the number "n" can be represented as √n and it cannot be simplified any further as it has only two factors 1 and the number itself(n). Hence, square root of 67 is simplified and written as √67. In this lesson, you will learn about square root of 67 by long division method along with solved examples.
Let us see what the square root of 67 is.
 Square Root of 67: √67 = 8.185
 Square of 67: 67^{2} = 4,489
1.  What Is the Square Root of 67? 
2.  Is Square Root of 67 Rational or Irrational? 
3.  How to Find the Square Root of 67? 
4.  FAQs on Square Root of 67 
What Is the Square Root of 67?
The square root of a number is the number that gets multiplied to itself to give the product. The square root of 67 is the value which we obtain after performing the operation of square root on 67.
Is the Square Root of 67 Rational or Irrational?
A number which can be expressed as a ratio of two integers, p/q such that q is not equal to 0 is known as a rational number. 67 cannot be dissociated into two such factors which on squaring give 67. It can be approximately written as a square of 8.185. It is a nonrecurring and nonterminating decimal number. This shows 67 isn't a perfect square which also proves that the square root of 67 is an irrational number.
Tips and Tricks:
 As square root of any number "n," which is not a perfect square, will always be an irrational number. Hence, 67 is a nonperfect square number and this concludes that square root of 67 is an irrational number.
How to Find the Square Root of 67?
Let us learn different ways of representing square root of 67.
 Simplified Radical Form of Square Root of 67
 Square root of 67 by Long Division Method
Click here to know more about the different methods.
Simplified Radical Form of Square Root of 67
The simplified radical form of square root of 67 is √67. As 67 is a prime number and has only two factors, it can be only broken into two factors 67 = 67 × 1. Hence, it cannot be simplified any further. Let us now try finding the square root of 67 by the long division method.
Square Root of 67 by Long Division Method
Let us understand the process of finding square root of 67 by long division.
 Step 1: Pair the digits of 67 starting with a digit at one's place. Put a horizontal bar to indicate pairing.
 Step 2: Now we find a number which on multiplication with itself gives a product of less than or equal to 67. As we know 8 × 8 = 64 < 67.
 Step 3: Now, we have to bring down 3 and multiply the quotient by 2. This give us 16. Hence, 16 is the starting digit of the new divisor.
 Step 4: 1 is placed at one's place of new divisor because when 161 is multiplied by 1 we get 161. The obtained answer now is 139 and we bring down 00.
 Step 5: The quotient now becomes 81 and it is multiplied by 2. This gives 162, which then would become the starting digit of the new divisor.
 Step 6: 8 is placed at one's place of new divisor because on multiplying 1628 by 8 we get 13024. The answer now obtained is 876 and we bring 00 down.
 Step 7: Now the quotient is 818 when multiplied by 2 gives 1636, which will be the starting digit of the new divisor.
 Step 8: 5 is placed at one's place of the divisor because on multiplying 16365 by 5 we will get 81825. The answer obtained is 5775 and we bring 00 down.
 Step 9: Now the quotient is 8185 when multiplied by 2 gives 16370, which will be the starting digit of the new divisor.
On repeating the steps, we can estimate the value of square root of 67 to as many places as required.
Explore square roots using illustrations and interactive examples
Important Notes:
 The square root is the inverse operation of squaring.
 Square root of 67 can be expressed as √67 or (67)^{1/2}.
 We can find the square root of 67 or any other number using the radical form and the long division method.
Square Root of 67 Solved Examples

Example 1: Evaluate whether √67 = √60 + √7 or not.
Solution
On simplifying LHS we get, √67 = 8.1853.
Similarly on simplifying RHS we get, √60 + √7 = 7.7459 + 2.6457 = 10.3916.
Hence, √67 ≠ √60 + √7. 
Example 2: What is the perimeter of a square having an area of 67 square inches?
Solution
The area of square is 67 square inches. And we know that, area of square = (side)^{2}. The length of side is obtained by taking square root of 67 which gives the value 8.18 inches.
Hence, the perimeter of square is given as 4 × (length) = 4 × 8.18 = 32.72 inches.
FAQs on Square Root of 67
What is the square root of 67 simplified?
As 67 can be only factorized as 67 = 67 × 1. Therefore the square root of 67 simplified is √67.
What is the square root of 67?
The square root of 67 is approximately 8.1853.
Is square root of 67 rational or irrational?
Since 67 is not a perfect square, and therefore it is an irrational number.
How do you find the square root of 67?
We can find the square root of 67 using the long division method.
Is square root of 67 a real number?
Yes, the square root of 67 is a real number.
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