76 has more than two factors. That has 2 and 19 together its prime factors and also the sum of the prime components is 21. In this lesson, us will discover to calculate the square root of 76 through long department method. Us will additionally go through a few solved examples and interactive inquiries related come the square root of 76.

You are watching: Square root of 76 in simplest radical form

Square root of 7676 = 8.717Square that 76: 762 = 5,776
1.What Is the Square source of 76?
2.Is Square source of 76 reasonable or Irrational?
3.Tips and also Tricks
4.How to discover the Square source of 76?
5.FAQs on Square source of 76

What Is the Square source of 76?

Square source of 76 is the number the when multiplied by itself results in the original number. As there is no together integer i beg your pardon on multiplying v itself offers 76 exactly, the square source of 76 is no a entirety number. 

Is the Square root of 76 rational or Irrational?

76 = 8.71779788 is a non-recurring and also non-terminating decimal number. Top top squaring 8.71779788, us get (8.71779788)2 = 75.999999. This value is around 76. This shows that 76 is not a perfect square which also proves that the square source of 76 is an irrational number.

Tips and Tricks:

76 is no a perfect square as the square root of 76 is one irrational number. The square root of any type of number n, i m sorry is no a perfect square, will always be an irrational number.

How to find the Square source of 76?

To uncover the square source of 76, we can use the following steps:

Step 1: First, we will check whether the number is a perfect square or not. 76 is no a perfect square together it can not be expressed together the square of a number.Step 2: as soon as the number is checked, we have the right to do the following:A number which is a perfect square can be created as x2 = x.For a number which is not a perfect square, the square root can be uncovered using the long department method. This number can be created in its simplified radical kind of the square root.

76 is no a perfect square. Hence, we will uncover the square source of 76 using the long division method. The streamlined radical type of the square root of 76 is offered below.

Simplified Radical form of Square root of 76

76 can be written as the product of 2 and 38. The is given as:

76 = (2 × 38)

2 is not a perfect square. Hence, it remains within the root sign. 38 deserve to be shown as 2 × 19. The streamlined radical type of the square source of 76 is 219.

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Square root of 76 by Long division Method

The square root of 76 deserve to be found using the long division method. These room the actions to it is in followed: 

Step 1: We begin pairing the digits from the right. We will pair up the number by placing a bar above them.Step 2: We require to uncover a number together that when it is multiplied with itself, the product is much less than or equal to 76. Keeping the divisor as 8, we gain the quotient together 8 and the remainder 76-64 = 12. Step 3: twin the divisor and enter it with a empty on the right. Then assume the biggest digit to change the blank; this will come to be the new digit in the quotient. Now, when the brand-new divisor will be multiply to the brand-new quotient, the final product will be lesser than or equal to our dividend. Finally, divide and also write the remainder. Carry down a pair the zeros to type the new dividend. Repeat this procedure to acquire the decimal places you want. 


Hence, √76 = 8.717

Explore square roots utilizing illustrations and interactive examples

Challenging Questions:

How will Justin discover the square source of 76 using the long division method as much as 8 decimal places?How will Shawn express the square source of 38 in terms of the square source of 76?