This lesson will teach us how to calculate the square root of 76 using the long division method. We will also go through a few interactive questions and solved examples related to the square root of 76. It has more than two factors, including the prime factors 2 and 19. Additionally, we will learn about the sum of prime factors of 21.

## What Is the Square Root of 76?

There is no integer such that when it is multiplied by itself and the resulting number is multiplied by the original number, it gives exactly 76.

## Square Root of 76 Solved Examples

Example 1: Calculate (2√19 + √76) × (4√19 – √76).

**Solution**

√76 can be simplified as 2**√**19

Hence, (2**√**19 + √76) = (2**√**19 + 2**√**19) = 4**√**19

(4**√**19 – √76) = (4**√**19 – 2**√**19) = 2**√**19

For finding (2**√**19 + √76) × (4**√**19 – √76), we take the product of the above obtained answers which gives (2**√**19 + √76) × (4**√**19 – √76) = 4**√**19 × 2**√**19 = 8 × 19 = 152.

Example 2: If the area of a circle is 76π square inches, what is its circumference?

**Solution**

The area of a circle is given as πr^{2}.

Hence, area = πr^{2} = 76π ⇒ r^{2} = 76 ⇒ r = **√**76 = 8.717 ≈ 8.7 inches.

Circumference of circle = 2πr = 2 × π × 8.7 = 54.63 inches. Thus, the circumference of the circle is 54.66 inches.

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## Interactive Questions

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## Is the Square Root of 76 Rational or Irrational?

The square root of 76 is an irrational number, which also proves that 76 is not a perfect square. This shows that the value of 76 is approximately 75.999999 (8.71779788)^2. By squaring 8.71779788, we get 76, indicating that 8.71779788 is a non-terminating and non-recurring decimal.

Here are some helpful tips and tricks:

## How to Find the Square Root of 76?

To calculate the square root of 76, we can utilize the subsequent procedures:.

The simplified radical form of the square root of 76 is provided below. By employing the long division technique, we will determine the square root of 76. Consequently, 76 does not possess the property of being a perfect square.

### Simplified Radical Form of Square Root of 76

76 can be expressed as the multiplication of 2 and 38. It is provided as: .

The square root of 76 is equal to the square root of 2 multiplied by 38.

The simplified radical form of the square root of 76 is 2√19. 2 × 19 can be expressed as 38. It remains within the root sign, therefore, 2 is not a perfect square.

### Square Root of 76 by Long Division Method

The technique of long division can be employed to determine the square root of 76. Here are the sequential instructions that must be adhered to:

Therefore, the square root of 76 is equal to 8.717.

Discover the concept of square roots through visual representations and engaging interactive demonstrations.

Challenging Questions:.

## FAQs on Square Root of 76

### What is the square root of 76 in the simplest form?

The simplest form representation of the square root of 76 is 2√19.

### How do you find the square root of 76?

Since 76 is not a perfect square, its square root can be calculated using the long division technique.

### What is the approximate square root of 76?

The approximate value of the square root of 76 is 8.71779788.

### Is the square root of 76 rational or irrational?

The square root of 76 is not a rational number.

### Is the square root of 76 a real number?

Yes, the square root of 76 is a valid number.