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Square Root of 43
The square root of 43 is expressed as √43 in the radical form and as (43)^{½} or (43)^{0.5} in the exponent form. The square root of 43 rounded up to 8 decimal places is 6.55743852. It is the positive solution of the equation x^{2} = 43.
 Square Root of 43: 6.557438524302
 Square Root of 43 in exponential form: (43)^{½} or (43)^{0.5}
 Square Root of 43 in radical form: √43
1.  What is the Square Root of 43? 
2.  Is Square Root of 43 Rational or Irrational? 
3.  How to Find the Square Root of 43? 
4.  FAQs on Square Root of 43 
What is the Square Root of 43?
The square root of a number is a number which when multiplied by itself, results in the original number. For example, the square root of 25 is 5, as 5 times 5 results in 25 which makes it a perfect square. However, you can also have square roots of some numbers that do not result in whole numbers, such as 43. We can express the square root of 43 in different ways as:
 Decimal form: 6.557
 Radical form: √43
 Exponent form: (43)^{1/2}
Is the Square Root of 43 Rational or Irrational?
 43 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 43 is an irrational number.
How to Find the Square Root of 43?
Since we concluded that the square root of 43 is nonterminating, we can only use 2 methods to calculate the value of its square root
 Long Division Method
 Estimation and Approximation Method
Long Division Method
 Step 1: Starting from the right, we will pair up the digits 43 by putting a bar above them. We also pair the 0s in decimals in pairs of 2 from left to right.
 Step 2: Think of a number whose square is less than or equal to 43. In this case, that number would be 6.
 Step 3: Dividing by 43 by 6 with quotient set as 6, we get a remainder of 7.
 Step 4: Drag a pair of 0’s down and fill it next to 7 to make the dividend 700.
 Step 5: The divisor, in this case 6 is doubled and written below. Now, we have 12X as the new divisor, and we need to find a value of X that makes the product of 12X × X less than or equal to 700. In this case, 125 is the required value
 Step 6: The number 5 is placed in the quotient after a decimal place. The new divisor for the next division will be 125 + 5 = 130.
Proceeding in the same manner and repeating from step 4, we can calculate the rest of the decimals.
Therefore, the square root of 43 = 6.557
Estimation and Approximation Method
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 that is smaller than and bigger than 43. In this case, 6 and 7 will work as their squares are 36 and 49.
 Step 2: Writing in terms of inequality 6 < √43 < 7 = 36 < 43 < 49
 Step 3: Multiply by 100 and write in terms of square roots √3600 < √4300 < √4900
 Step 4: Move closer to inequality √4225 < √4300 < √4356 = 65 < 10√43 < 66 = 6.5 < √43 < 6.6
 Step 5: Taking average of upper and lower limits we get, (6.5 + 6.6)/2 = 6.55
Therefore, we can estimate the square root of 43 ≅ 6.55
Explore Square roots using illustrations and interactive examples
Challenging Questions
 Determine the value of the following:
 √0.43
 √4343
 What are the roots of 43? Also find the value of the square of the negative root of 43.
Important Notes
 The real roots of √43 are ± 6.557.
 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.
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 43 square inches. Help him find the length, rounded to the nearest tenth.
Solution:
To find the side of the land, we will have to find the square root of 43. The square root is √43 = 6.557.
Hence, the side length of the garden is approximately 6.6 inches. 
Example 2: What is the circumference of a circle whose area is 43π inches^{2}?
Solution:
Let circumference of circle be denoted by C, area by A, and radius length by r.
C = 2πr
A = πr^{2}
43π = πr^{2}
Simplifying we get, r^{2} = 43 which implies r = √43
C = 2πr = 2π × √43 = 41.20 inches.Therefore, the circumference of circle is about 41.20 inches.

Example: If the area of a circle is 43π in^{2}. Find the radius of the circle.
Solution:
Let 'r' be the radius of the circle.
⇒ Area of the circle = πr^{2} = 43π in^{2}
⇒ r = ±√43 in
Since radius can't be negative,
⇒ r = √43
The square root of 43 is 6.557.
⇒ r = 6.557 in
FAQs on the Square Root of 43
What is the Value of the Square Root of 43?
The square root of 43 is 6.55743.
Why is the Square Root of 43 an Irrational Number?
The number 43 is prime. This implies that the number 43 is pairless and is not in the power of 2. Therefore, the square root of 43 is irrational.
Evaluate 15 plus 5 square root 43
The given expression is 15 + 5 √43. We know that the square root of 43 is 6.557. Therefore, 15 + 5 √43 = 15 + 5 × 6.557 = 15 + 32.787 = 47.787
What is the Square Root of 43?
The square root of 43 is an imaginary number. It can be written as √43 = √1 × √43 = i √43 = 6.557i
where i = √1 and it is called the imaginary unit.
If the Square Root of 43 is 6.557. Find the Value of the Square Root of 0.43.
Let us represent √0.43 in p/q form i.e. √(43/100) = 0.43/10 = 0.656. Hence, the value of √0.43 = 0.656
What is the Square Root of 43 in Simplest Radical Form?
The number 43 is a prime number. This implies that the number 43 is pairless and is not in the power of 2. Therefore, the radical form of square root of 43 cannot be simplified further.
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