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Square Root of 23
The square root of 23 is expressed as √23 in the radical form and as (23)^{½} or (23)^{0.5} in the exponent form. The square root of 23 rounded up to 7 decimal places is 4.7958315. It is the positive solution of the equation x^{2} = 23.
 Square Root of 23: 4.795831523312719
 Square Root of 23 in exponential form: (23)^{½} or (23)^{0.5}
 Square Root of 23 in radical form: √23
1.  What Is the Square Root of 23? 
2.  Is Square Root of 23 Rational or Irrational? 
3.  How to Find the Square Root of 23? 
4.  Important Notes 
5.  Think Tank 
6.  FAQs on Square Root of 23 
What Is the Square Root of 23?
The square root of a number n is written as √n. This number when squared or multiplied by itself results in the original number n. The square root of 23 can be written in multiple ways.
 Radical form: √23
 Decimal form: 4.796
 Exponent form: (23)^{1/2}
Is Square Root of 23 Rational or Irrational?
 23 is a number that is not a perfect square, meaning it does not have a natural number as its square root.
 Also, its square root cannot be expressed as a fraction of the form p/q which tells us that the square root of 23 is an irrational number.
How to Find the Square Root of 23?
There are only 2 ways to find the square root of 23:
 Long Division Method
 Estimation and Approximation
We cannot use the prime factorization method here, as 23 is a prime number. Think about it.
Long Division Method
The square root of 23 by long division method consists of the following steps:
 Step 1: Starting from the right, we will pair up the digits 23 by putting a bar above them. We also pair the 0s in decimals in pairs of 2 from left to right.
 Step 2: Find a number that, when multiplied to itself, gives a product less than or equal to 23. The number 4 fits here as 4 squared gives 16. Dividing 23 by 4 with the quotient as 4, we get the remainder as 7.
 Step 3: Drag a pair of 0s down and fill it next to 7 to make the dividend 700.
 Step 4: Double the divisor 4, and enter 8 below with a blank digit on its right. Guess the largest possible digit(X) to fill in the blank and the quotient for which the product of 8X and X results in a value less than or equal to 700. Since 7 fits the value of X, we fill 7 in the quotient after the decimal point. Divide and write the remainder.
 Step 5: Repeat this process to get the decimal places you want.
Therefore, the square root of 23 = 4.7958
Estimation and Approximation
The estimation method gives us an approximate answer and is usually not accurate to more than 1 decimal place. However, it is easy to perform as can be seen under.
 Step 1: Find a perfect square which is smaller than and bigger than 23. In this case, 4 and 5 will work as their squares are 16 and 25.
 Step 2: Writing in terms of inequality 4<√23<5 = 16<23<25
 Step 3: Multiply by 10 and write in terms of square roots √1600<√2300<√2500
 Step 4: Move closer to inequality √2209<√2300<√2304 = 47<10√23<48
= 4.7<√23<4.8  Step 5: Taking the average of upper and lower limits we get, (4.7 + 4.8)/2 = 4.75
Therefore, we can estimate the square root of 23 ≅ 4.75
Explore square roots using illustrations and interactive examples
Important Notes
 There exists a positive and negative root of 23, 4.7958 and 4.7958.
 The square root of 23 is an irrational number that is nonterminating.
 There will be n/2 digits in the square root of an even number with n digits.
 There will be (n+2)/2 digits in the square root of an odd number with n digits.
Think Tank
 Can you think of a quadratic equation that has a root of √23?
 Since ((√23)^{2} = 23, can we say that √23 is also a square root of 23?
Solved Examples

Example 1: Andy wants to calculate the side length of the square shape he made in arts and craft class. It has an area of 23 square centimeters.
Solution:
 To find the side of the land, we will have to find the square root of 23.
 The square root is √23 = 4.795.
 Hence, the side length of the garden is approximately 4.8 cm.

Example 2: Matt is trying to solve the equation  x^{2}  529 = 0. Help him find all values of x
Solution:
x^{2}  529 = 0
x^{2} = 529.
Taking the square root on both sides, we get
x = ±23 
Example 3: If the area of a circle is 23π in^{2}. Find the radius of the circle.
Solution:
Let 'r' be the radius of the circle.
⇒ Area of the circle = πr^{2} = 23π in^{2}
⇒ r = ±√23 in
Since radius can't be negative,
⇒ r = √23
The square root of 23 is 4.796.
⇒ r = 4.796 in
FAQs on the Square Root of 23
What is the Value of the Square Root of 23?
The square root of 23 is 4.79583.
Why is the Square Root of 23 an Irrational Number?
The number 23 is prime. This implies that the number 23 is pairless and is not in the power of 2. Therefore, the square root of 23 is irrational.
Is the number 23 a Perfect Square?
The number 23 is prime. This implies that the square root of 23 cannot be expressed as a product of two equal integers. Therefore, the number 23 is not a perfect square.
What is the Square Root of 23 in Simplest Radical Form?
The number 23 is a prime number. This implies that the number 23 is pairless and is not in the power of 2. Therefore, the radical form of square root of 23 cannot be simplified further.
What is the Value of 18 square root 23?
The square root of 23 is 4.796. Therefore, 18 √23 = 18 × 4.796 = 86.325.
Evaluate 16 plus 14 square root 23
The given expression is 16 + 14 √23. We know that the square root of 23 is 4.796. Therefore, 16 + 14 √23 = 16 + 14 × 4.796 = 16 + 67.142 = 83.142
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