# Square Root of 40 | Top Q&A

Square Root of 40 The square root of a number is always a positive and negative value pair of a given number. The square root of 40 implies a number that when multiplied by itself gives 40. Now we’re going to calculate the square root of 40 using approximation and long division along with some interesting math problems.

**Square root of 40: 40 = 6.3245****Square 40: 40² = 1600**

1. What is the square root of 40? 2. Is the square root of 40 Reasonable or Unreasonable? 3. How to Find the Square Root of 40? 4. Important Notes on Square Root of 40 5. Challenging Questions 6. Frequently Asked Questions about Square Root of 40

- The square root of any number is a number that when multiplied by itself gives a given number.
- The square root of 40 is expressed as √40 = 6.3245
- Square root of 40 in root form = 40 = (2 × 2 × 2 × 5) = 2√10
- Therefore, 40 is not a perfect square

- A number is defined as a rational number when it can be expressed as p/q where q ≠ 0.
- Because the square root of 40 is a non-terminating and non-repeating number. So the square root of 40 cannot be represented as p/q.
- Therefore, the square root of 40 is an irrational number.

We can calculate the square root of 40 using the approximation method or the long division method.

### Square root of 40 by approximation

- First, we need to find two perfect squares between which 40 lie.
- We know that 36 (62) and 49 (72) are two perfect squares between 40 lying.
- So the square root of 40 will be greater than 6 but less than 7.6. 6 < √40 < 7 Hence, the integer part of the number will be 6.
- For the decimal part, we will use the formula: Given numbers – Lower perfect square / Greater than perfect square – Lower perfect square = (40-36) / (49-36) = 4/ 13 = 0.31 So approx. The square root of 40 would be 6.31

### Square Root of 40 by Long Division

By following the steps below, we can find the square root of 40 using the long division method.**Step 1.** Write 40 as shown below in the diagram. Start matching numbers from one’s position into pairs of two by placing a stick on top of them. **Step 2.** Now find a number such that when multiplied by itself the result is a number less than 40. We know that 6 × 6 = 36 **Step 3.** Now subtract it from the divisor as done in normal division and add the divisor to itself calculated in the previous step. The divisor will become 12 and the remainder will be 4. **Step 4. **Since there are no more numbers in the divisor, we put a decimal point after the divisor and quotient simultaneously. Now put three pairs of zeros after the decimal in the dividend and reduce the first pair of zeros. **Step 5.** Now find a number in the place of the unit divisor such that the result is a number less than 400. Here the number will be 3 because 123 × 3 = 369 (less than 400) **Step 6.** Bring down the next pair of zeros and repeat the steps until the last pair of zeros.Thus, we get the square root of √40 = 6,324 using the long division method.

- Square root of 400
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- The square root of 40 is expressed as √40 in root form.
- There will be n/2 digits in the square root of an even number of n digits.
- There will be (n + 2) / 2 digits in the square root of an odd n digit number
- The square root of 40 is written as (40) 1/2 as an exponent.

- How much must 40 be divided in order for it to be a perfect cube?
- Find the square root of all the factors of 40?

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