What is the square root of 40? | How to find the square root of 40?

The square root of 40 is 6.3245 mentioned with a symbol √. The square root of 40 is denoted using √40 or 401/2. In the radical form, the square root of 40 is represented as 2√10.

The square root of a number is determined when a quantity of a number is produced when multiplied by itself or a factor of a number when multiplied by itself gives the original number. In simple terms when a value is multiplied by itself it gives the original number.

For a better understanding,
The number 8 when multiplied by itself (8× 8) = 64. The square root for  (64) is 8. 
The square root of √40 = 40210
The square root of √40 in decimal form,
√40=  6.3245
The square root of √40 in exponent form, 
40^1/2= 6.3245

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The calculation for the square root of 40

• The square root of a number is when the given number is multiplied by itself it should produce the original number. 
• The given number 40 cannot be expressed as p/q and is an irrational number. 
• To find the square root of any number first the given number is usually checked to determine whether they are a perfect square number or not. 
• The square root of the irrational number is found using the long division method.
• For the numbers with a perfect square, it is easy to find the square roots and it is a bit tough for non-square values. Numbers like 4,9, 16,25, etc., are perfect squares. 
• Numbers that end with 2,3,7,18 and 40 are not perfect square numbers.

Methods to find the square root

There are three methods to find the square root of a number

• Prime factorization method
• Long division method
• Repeated subtraction

These methods described above do not apply to finding the square root of any number.  

Prime factorization method

To find the square root of a number using the prime factorization method first knows the prime factors of the numbers. Let us take n as a prime number, by grouping their squares we get n² now multiplying them we get the square root of the number. 

• Step 1: Find the prime factor for the given number
  40 = 2×2×2×5
• Step 2: Pair the prime factors.
  40 = 2² ×2×5
  Take square on both sides
  √ 40= √ (2)² ×√ 2×√ 5
  You can cancel the square with the square root we get
  √40 = √2×√2×√5
• Step 3: Multiply the factors
  The √2 = 1.414
  √5 = 2.236
  √40 = 2.236 ×1.4142
  √40 = 6.3245

Long division method

Long division is one of the easiest methods to find the square root of any number. It was the preferred method to be used for the non-perfect square numbers. Find the integer that can divide the number and proceed with the long division. 

Steps to find the square root of 40:

• Step 1: Find the smallest integer that can divide the number. 
• Step 2: Keep following the long division using divisor and dividend. 
• Step 3: When the particular number of satisfaction is reached the quotient is the square root of the number.  

Find the square root of 40

• Step 1: Find the smallest integer that can divide the number. 40 is not a perfect root number and 6 is the nearest number that can divide it. 
• Step 2: Keep following the long division using divisor and dividend. 

Long division for square root 40

• Step 3: When the particular number of satisfaction is reached the quotient is the square root of the number.
• Hence, the √40 = 6.324

Solved Examples

Example 1: Find the square root of 125 using the prime factorization method
Solution:
The prime factors of 125 = 5×5×5
√ 125 = 5√ 5
= 5 2.236
= ≈11.18
Hence, the √ 125 = 11.18.
Example 2: What is the square root of 1?
Solution:
The  √1 is 1. The multiplication of 1× 1 =1, the division of (1÷1)=1, the same goes for the square root of 1. 
The   √1 = 1. 
Example 3: What is the square root of 40 using long division methods?
Solution:

Hence, the √40 = 6.324
Example 4: What is an irrational number
Solution:
 A number is said to be an irrational number if it cannot be expressed in the form of a ratio or fractions. 
Example: √2, √3, √5 or √40
Example 5: Solve √4×√40
Solution:
The √40 = 6.324
√4 = 2
√16×√40 = 2 × 6.324
√4×√40 = 12.648

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FAQs on the square root of 40