Square Root 40 is 6.32456. Square Root of 40 is the which when multiplied by itself gives back 40 as the result. This means when 6.32456 is multiplied by 6.32456, the product is approximately equal to 40.

In this article, we will discuss what is the square of root 40, how to represent and how to find it using different methods.

What is the Square Root of 40?

Square Root of 40, is denoted as √40 and it is equal to 6.3245. So, the original positive number is ‘6.3245’ multiplied by itself 6.3245 × 6.3245 then we get the number 40. The Square Root of 40 is represented as follows:

• Square Root of 40 in Radical Form: √40 = 6.3245
• Square Root of 40 in Fractional Exponent Form: (40)^1/2 = 6.3245…

Square Root of 40 Calculator

Try out the following calculator to find the square root of 40

How to Calculate a Square Root of 40?

Some of the methods are given below to find out the square root of 40.

• Square Root of 40 by Long Division Method

• Square Root 40 by Prime Factorization Method

Square Root of 40 by Long Division Method

To compute the square root by long division method, the number’s root must be determined systematically. So, Let’s Calculate the square root of 40 by the long division method involves the following steps:

• Step 1: Let’s begin with the number 40, and start pairing it from right to left.
• Step 2: Choose a perfect square less than 40 as the initial dividend (e.g., 36). Hence divisor will be 6.
• Step 3:  Since the divisor is 6, the quotient is 6 therefore dividend will be 36. Subtract 36 from 40 and add 6 in the divisor.
• Step 4: New divisor is 12, dividend is 4. Now put decimal after 6 in quotient and bring down two zeros. Therefore new dividend is 400.
• Step 5: Add a digit at the left of 12 in the divisor i.e. at the unit place and also place the same digit in the quotient such that the product is near to 400.
• Step 6: Add 3 in the divisor using step 5 hence, the new dividend will be 123 × 3 = 369. Subtract 369 from 400.
• Step 7: Continue with this until the square root of 40 is obtained to three decimal places.

Therefore, the value of the square root of 40 approximately will be 6.324… so on.

Square Root 40 by Prime Factorization Method

Square root of 40 can be found easily using the following steps

• Step 1: Break down 40 into prime factors. Hence, √40 = 2 × 2 × 2 × 5 or 2³ × 5.
• Step 2: Now, Take one factor from each pair and multiply them together: √40 ​= √(2 × 2) × 2 × 5.
• Step 3: Then after combining the factors, √40 ​= √(4 × 2 × 5​)
• Step 4: After multiplying the numbers under square root will be √(4 × 10) = 2√10.

So, the square root of 40 is 2√10 by using the prime factorization method.

Is Square Root of 40 Rational or Irrational?

Since the square root of 40 is 6.32456…. is a non-terminating and non-repeating number. We know that the decimal of an irrational number is non-terminating and non-repeating. Therefore, the square root of 40 is an irrational number.

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