The square root of 77 is expressed together √77 in the radical type and together (77)½ or (77)0.5 in the exponent form. The square root of 77 rounded up to 7 decimal areas is 8.7749644. The is the positive solution the the equation x2 = 77.

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Square source of 77: 8.774964387392123Square root of 77 in exponential form: (77)½ or (77)0.5Square source of 77 in radical form: √77
1.What Is the Square root of 77?
2.Is Square root of 77 rational or Irrational?
3.How to uncover the Square source of 77?
4.Challenging Questions
5.FAQs top top Square root of 77

What Is the Square source of 77?


The square source of a number n is written as √n. This number when squared or multiply by itself results in the initial number n. The square root of 77 can be represented in the complying with ways.

Radical form: √77 Decimal form: 8.77496 Exponent form: (77)½

Is Square source of 77 Rational or Irrational?


Square source of 77 in the decimal kind is √77 = 8.77496

How to uncover the Square source of 77?


There are two ways to discover the square root of 77:

Long department MethodPrime factorization Method

Long division Method

The square root of 77 by long division method consists of the following steps:

Step 1: starting from the right, we will certainly pair up the digits 77 by placing a bar over 77. Us will likewise pair the 0s in the decimal from left come right.Step 3: traction a pair that 0’s down and place them next to 13 to do the dividend 1300.Step 4: dual the divisor 8, and also enter 16 below with a blank digit top top its right. Think of a number i beg your pardon is greater than or same to the dividend, i.e., 1300. 167 is the perfect number to division 1300.Step 6: Repeat this process until you gain the preferred number.

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Therefore, the square source of 77 = 8.77

Prime factorization Method

Since all the prime factors of 77 are unique, no one of these components are perfect squares. The square root of 77 cannot it is in simplified.Therefore, the square root of √77 = 8.77

Explore square roots using illustrations and also interactive examples


Challenging Questions


What is the an adverse root that 7700?Find the square root of 7700 as much as 5 decimal places.What is the square source of:a) 770b) 777

Solved Examples


Example 1: Jack is multiply a number through itself. If the product is 77, help Jack discover the number.

Solution:

To find the number, let united state assume the number come be zOn multiplying z times z = z × z = 77z² = 77z = √77z = 8.77(8.77 × 8.77 = 76.9129 ≅ 77)The number is 8.77.


Example 2: The area of a square-shaped table is 5929 square units. Calculation the size of one side of the table.

Solution: 

The area of the table = 5929 sq. UnitsTo uncover the next of a square-shaped table, let us take square source of 5929  by prime factorization method.√5929 = √(7 × 7 × 11 × 11) = 7 × 11Square source of 5929 is 77.Therefore, the length of the side of the square table is 77 units.


Example 3: assist Joy find the square root of 77 as much as 3 decimal places.

Solution: 

Step 1: beginning from the right, we will pair up the number 77 by place a bar over 77. Us will additionally pair the six 0s in decimals in bag of 2 from left to right.Step 2: discover a number that, as soon as multiplied come itself, offers a product less than or same to 77. The number 8 fits right here as 8 square gives 64. Separating 77 by 8 with quotient as 8, we obtain the remainder together 13.Step 3: drag a pair that 0’s down and also place them next come 13 to do the dividend 1300.Step 4: dual the divisor 8 and location 16 below with a empty digit come its right. Think of a number i m sorry is greater than or same to the dividend, i.e. 1300. 167 is the perfect number to divide 1300.Step 5: multiply 167 by 7 (167 × 7 = 1169 Step 6: Repeat this process up to three decimal places.

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FAQs top top the Square root of 77

What is the worth of the Square root of 77?

The square source of 77 is 8.77496.

Why is the Square root of 77 an Irrational Number?

Upon element factorizing 77 i.e. 71 × 111, 7 is in odd power. Therefore, the square source of 77 is irrational.

If the Square root of 77 is 8.775. Uncover the value of the Square root of 0.77.

Let us represent √0.77 in p/q form i.e. √(77/100) = 0.77/10 = 0.877. Hence, the value of √0.77 = 0.877

Evaluate 16 add to 9 square root 77

The offered expression is 16 + 9 √77. We recognize that the square source of 77 is 8.775. Therefore, 16 + 9 √77 = 16 + 9 × 8.775 = 16 + 78.975 = 94.975

What is the Square of the Square root of 77?

The square of the square root of 77 is the number 77 itself i.e. (√77)2 = (77)2/2 = 77.

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What is the Square root of -77?

The square source of -77 is an imaginary number. It have the right to be composed as √-77 = √-1 × √77 = i √77 = 8.774iwhere ns = √-1 and also it is called the imagine unit.