# Square Root of 76 – How to Find the Square Root of 76?

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.

• The square root of 76, denoted as √76, is equal to 8.717.
• The product of 76 squared, which is 762, equals 5,776.

## 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 219

Hence, (219 + √76) = (219 + 219) = 419

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(419 – √76) = (419 – 219) = 219

For finding (219 + √76) × (419 – √76), we take the product of the above obtained answers which gives (219 + √76) × (419 – √76) = 419 × 219 = 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 πr2.

Hence, area = πr2 = 76π ⇒ r2 = 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

Verify Response >.

## 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:

• The square root of any non-perfect square number n will always be an irrational number. As 76 is not a perfect square, its square root is also an irrational number.
• ## How to Find the Square Root of 76?

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

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• 76 cannot be expressed as a perfect square number.
• Step 2: After verifying the number, we can proceed with the following steps:
• A number that is a perfect square can be expressed as √x2 = x.
• The simplified radical form of this number’s square root can be expressed using the long division method, if the number is not a perfect square.
• 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:

• Step 1: We start pairing the digits from the right. We will pair up the digits by placing a bar above them.
• In order to find a number such that when it is multiplied by itself and the product is subtracted from 76, the remainder is equal to 12 and the quotient is 8, we need to follow a 2-step process.
• Repeat this process to obtain the decimal places you want. Bring down a pair of zeros to form the new dividend. Finally, write the remainder and divide. The final product will be equal to or lesser than our dividend. The final product will be equal to or lesser than our dividend. This will become the new digit in the quotient; assume the largest digit to replace the blank. Then, enter it with a blank on its right and double the divisor: 3.
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Therefore, the square root of 76 is equal to 8.717.

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

• The square root of 576 is 24.
• The square root of 38.
• The square root of 676 is 26.
• The square root of 75.
• The square root of 74.
• Challenging Questions:.

• How will Justin determine the square root of 76 utilizing the long division technique up to 8 decimal points?
• How will Shawn represent the square root of 38 in relation to the square root of 76?
• ## 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.

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