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Square Root of 47
The square root of 47 is a number which when multiplied by itself, results in the number 47. 47 is also a prime number which makes it trickier to calculate its square root. We will learn how to calculate the square root of 47 and look at a few problems to help us understand this topic.
Square Root of 47: √47= 6.8556546...
Square of 47: 47^{2} = 2209
1.  What is the Square Root of 47? 
2.  Is Square Root of 47 Rational or Irrational? 
3.  How to Find the Square Root of 47? 
4.  FAQs on Square Root of 47 
What is the Square Root of 47?
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 47. We can express the square root of 47 in different ways
 Decimal form: 6.856
 Radical form: √47
 Exponent form: (47)^{1/2}
Is the Square Root of 47 Rational or Irrational?
 47 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 47 is an irrational number.
How to Find the Square Root of 47?
Since we concluded that the square root of 46 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
 Step 1: Starting from the right, we will pair up the digits 47 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 47. In this case, that number would be 6.
 Step 3: Dividing by 47 by 6 with quotient set as 6, we get a remainder of 11.
 Step 4: Drag a pair of 0’s down and fill it next to 11 to make the dividend 1100.
 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 1100. In this case, 128 is the required value
 Step 6: The new divisor for the next division will be 128 + 8 = 136. The number 5 is placed in the quotient after a decimal place. The new divisor for the next division is 1365.
Proceeding in the same manner and repeating from step 4, we can calculate the rest of the decimals.
Therefore, the square root of 47 = 6.856
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 that is smaller than and bigger than 47. In this case, 6 and 7 will work as their squares are 36 and 49.
 Step 2: Writing in terms of inequality 6<√47<7 = 36<47<49
 Step 3: Multiply by 100 and write in terms of square roots √3600<√4700<√4900
 Step 4: Move closer to inequality √4624<√4700<√4761 = 68<10√47<68
= 6.8<√47<6.9  Step 5: Taking average of upper and lower limits we get, (6.8 + 6.9) / 2 = 6.85
Therefore, we can estimate the square root of 47 ≅ 6.85
Explore Square roots using illustrations and interactive examples
Challenging Questions
 What is the square root of 47 up to 6 decimal places(Use Long Division)
 What are the roots of 47? Also, find the value of the square of the negative root of 47
Solved Examples

Example 1: Zack wants to calculate the diagonal length of the garden at his home. It has an area of 47 square units. Help him find the length, rounded to the nearest tenth.
Solution:
To find the side of the garden, we will have to find the square root of 47.
Diagonal Length = √2 × Side Length = √2 × √47 = √94 = 9.695
Therefore, the diagonal length of the garden is 9.7 units. 
Example 2: What is the circumference of a circular indoor cycling track whose area is 47π square units?
Solution:
Let Circumference be denoted by C, Area by A, and radius length by r
C = 2πr
A = πr^{2}
47π = πr^{2}
Simplifying we get, r^{2} = 47 which implies r = √47
C = 2πr = 2π × √47 = 43.07 unitsTherefore, the perimeter of the land is about 43.07 units
FAQs on Square Root of 47
What is the square root of 47?
The square root of 47 is √47= 6.856.
Is the square root of 47 a rational number?
No, the square root of 47 is not a rational number since the square root of 47 is nonterminating and cannot be represented in the form of p/q.
What is the square root of 47 in the simplest radical form?
√47 is the simplest radical form.
What is the square of 47?
The square of 47 is 47^{2} = 2209
What is the value of √47 times √47?
The value of √47 times √47 is 47.
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