Square Root of 71
Did you know 71 is a prime number? When we find the square root of 71, we can see that it cannot be simplified any further as it has only two factors 1 and the number itself(71). Hence, square root of 71 is simplified and written as √71. In this lesson, you will learn about square root of 71 by long division method along with solved examples.
Let us see what the square root of 71 is.
 Square Root of 71:√71 = 8.426
 Square of 71: 71^{2} = 5,041
1.  What Is the Square Root of 71? 
2.  Is Square Root of 71 Rational or Irrational? 
3.  How to Find the Square Root of 71? 
4.  FAQs on Square Root of 71 
What Is the Square Root of 71?
The square root of 71 is the number that gets multiplied to itself to give the product as 71.
Is the Square Root of 71 Rational or Irrational?
A rational number can be expressed as a ratio of two integers, p/q such that q is not equal to 0. As we know, 71 cannot be brokeninto two such factors which on squaring give 71. It can be approximately written as a square of 8.426 and it is a nonrecurring and nonterminating decimal number. Hence, 71 isn't a perfect square and the square root of 71 is an irrational number.
Tips and Tricks:
 71 is a prime number which makes it a nonperfect square number too. As we know, square root of any number "n," which is not a perfect square, will always be an irrational number. Thus square root of 71 is an irrational number.
How to Find the Square Root of 71?
Let us learn different ways of representing square root of 71.
 Simplified Radical Form of Square Root of 71
 Square root of 71 by Long Division Method
Click here to know more about the different methods.
Simplified Radical Form of Square Root of 71
The simplified radical form of square root of 71 is √71. As 71 is a prime number and it has only two factors. Hence, it can be only broken into two factors 71 = 71 × 1. Hence, we cannot simplify it any further. Let us now try finding the square root of 71 by the long division method.
Square Root of 71 by Long Division Method
Let us understand the process of finding square root of 71 by long division.
 Step 1: Pair the digits of 71 starting with a digit at one's place and 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 71. As we know 8 × 8 = 64 < 71.
 Step 3: Now, we have to bring down 7 and multiply the quotient by 2. This give us 16. Hence, 16 is the starting digit of the new divisor.
 Step 4: 4 is placed at one's place of new divisor because when 164 is multiplied by 4 we get 656. The obtained answer now is 44 and we bring down 00.
 Step 5: The quotient now becomes 84 and it is multiplied by 2. This gives 168, which then would become the starting digit of the new divisor.
 Step 6: 2 is placed at one's place of new divisor because on multiplying 1682 by 2 we get 3364. The answer now obtained is 1036 and we bring 00 down.
 Step 7: Now the quotient is 842 when multiplied by 2 gives 1684, which will be the starting digit of the new divisor.
 Step 8: 6 is placed at one's place of the divisor because on multiplying 16846 by 6 we will get 101076. The answer obtained is 2526 and we bring 00 down.
 Step 9: Now the quotient is 8426 when multiplied by 2 gives 16852, which will be the starting digit of the new divisor.
We can estimate the value of square root of 71 to as many places as required using the same steps as discussed above.
Explore square roots using illustrations and interactive examples
Important Notes:
 The square root is the inverse operation of squaring.
 The square root of 71 is expressed as √71 or (71)^{1/2}.
 We can find the square root of 71 by using the radical form and the long division method.
Square Root of 71 Solved Examples

Example 1: Prove that square root of 71 is not equal to the sum of square root of 70 and square root of 1.
Solution
As per the statement, we need to prove √71 ≠ √70 + √1.
On simplifying LHS we get, √71 = 8.4261.
Similarly on simplifying RHS we get, √70 + √1 = 8.4261 + 1 = 9.4261.
Thus, √71 ≠ √70 + √1.Hence Proved

Example 2: What is the length of side of square having an area 71 square inches?
Solution
The area of square is 71 square inches. And we know that, area of square = (side)^{2}.
Hence, the length of side is obtained by taking square root of 71 which gives the value 8.42 inches.
FAQs on Square Root of 71
What is the square root of 71 simplified?
As 71 can be only factorized as 71 = 71 × 1. Therefore the square root of 71 simplified is √71.
What is the square root of 71?
The square root of 71 is approximately 8.426.
Is square root of 71 rational or irrational?
Since 71 is not a perfect square, and therefore it is an irrational number.
How do you find the square root of 71?
We can find the square root of 71 using the long division method.
Is square root of 71 a real number?
Yes, the square root of 71 is a real number.