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Square Root of 91
The square root of 91 is expressed as √91 in the radical form and as (91)^{½} or (91)^{0.5} in the exponent form. The square root of 91 rounded up to 10 decimal places is 9.5393920142. It is the positive solution of the equation x^{2} = 91.
 Square Root of 91: 9.539392014169456
 Square Root of 91 in exponential form: (91)^{½} or (91)^{0.5}
 Square Root of 91 in radical form: √91
1.  What Is the Square Root of 91? 
2.  Is the Square Root of 91 Rational or Irrational? 
3.  How to Find the Square Root of 91? 
4.  FAQs on Square Root of 91 
What Is the Square Root of 91?
 The square root of a number is the number that when multiplied to itself gives the original number as the product.
 n × n = 91. This shows square of a number is 91.
 n = √91 or n = 91^{½}
 The simplified form of the Square Root of 91 is √91
Is the Square Root of 91 Rational or Irrational?
 A rational number is defined as a number that can be expressed in the form of a quotient or division of two integers, i.e. p/q, where q is not equal to 0.
 The value of √91 is evaluated as 9.539392014169456
 Therefore √91 is irrational.
How to Find the Square Root of 91?
The square root of 91 can be calculated using different methods such as prime factorization or the long division method or the average method.
Square Root of 91 by Approximation Method
 Find 2 perfect squares closest to 91. They are 81 and 100. 81 < 91 < 100
 √81 < √91 < √100
 9 < √91 < 10
 Divide 91 by 9 or 10. let's divide by 9. 91 ÷ 9 = 10.11
 Find the average of this quotient and the 9. (10.11 + 9) ÷ 2
 19.11 ÷ 2 = 9.55
 Thus √91 ≈ 9.55
Square Root of 91 by Long Division Method
 Write 91 in pairs after the decimal point as 91. 00 00 00.
 Find a (number × number) that it gives 91 or less than that. We find 9 × 9 = 81. subtract 81 from 91 and obtain 10 as the remainder.
 Bring down the next pair of zeros. 10 00 becomes the new dividend.
 Double the quotient. It is 18. Now 180 is written in the new divisor's place.
 Find a (number+ 180) × number ≤ 10 00. We determine that 180 + 5 = 185 and 184 × 5 = 925.
 Subtract this from 1000. It is 75 and get the new divisor by brining down the next pair of zeros. 7500 is our new dividend.
 Repeat the process until we approximate the value to 3 decimal places.
 Thus, √91 = 9.539
Explore Square roots using illustrations and interactive examples
Tips and Tricks
 Know that 91 lies between the perfect squares 81 and 100 and hence the square root of 91 lies between 9 and 10.
 Use the average method to approximate the square root of 91.
Important Notes
 The square root of 91 is expressed as √91 in the radical form and as 91^{½} in the exponential form.
 √91= ± 9.539392014169456
Square Root of 91 Solved Examples

Example 1: Jolly thinks of a number. One seventh of a square of the number is 13. What could be the number approximated to hundredths?
Solution:
One seventh of a square of a number = 1/7 n^{2} = 13
n^{2} = 7 × 13 = 91
n = √91
= ± 9.5393 = 9.54
The number is 9.54 
Example 2 : What number should Roy add to 91 to obtain a perfect square number? Find the square root of the resulatant number and the number adding. Are both perfect squares?
Solution:
Square root of 91 lies betwwen 9 and 10.
We know that,
Square of 9 = 81
Square of 10 = 100.
91 lies between 81 and 100.
On adding number 9 to 91 we have,
91 + 9 = 100
Square root of 100 is 10.
Square root of 9 is 3.
Yes 100 and 9 both the numbers are perfect square. 
Example: If the surface area of a cube is 546 in^{2}. Find the length of the side of the cube.
Solution:
Let 'a' be the length of the side of the cube.
⇒ Area of the cube = 6a^{2} = 546 in^{2}
⇒ a = ±√91 in
Since length can't be negative,
⇒ a = √91
We know that the square root of 91 is 9.539.
⇒ a = 9.539 in
FAQs on the Square Root of 91
What is the Value of the Square Root of 91?
The square root of 91 is 9.53939.
Why is the Square Root of 91 an Irrational Number?
Upon prime factorizing 91 i.e. 7^{1} × 13^{1}, 7 is in odd power. Therefore, the square root of 91 is irrational.
What is the Square of the Square Root of 91?
The square of the square root of 91 is the number 91 itself i.e. (√91)^{2} = (91)^{2/2} = 91.
Is the number 91 a Perfect Square?
The prime factorization of 91 = 7^{1} × 13^{1}. Here, the prime factor 7 is not in the pair. Therefore, 91 is not a perfect square.
What is the Square Root of 91?
The square root of 91 is an imaginary number. It can be written as √91 = √1 × √91 = i √91 = 9.539i
where i = √1 and it is called the imaginary unit.
Evaluate 5 plus 8 square root 91
The given expression is 5 + 8 √91. We know that the square root of 91 is 9.539. Therefore, 5 + 8 √91 = 5 + 8 × 9.539 = 5 + 76.315 = 81.315
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