Square Root of 77

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

• Square Root of 77: 8.774964387392123
• Square Root of 77 in exponential form: (77)^½ or (77)^0.5
• Square Root of 77 in radical form: √77

The square root of a number n is written as √n. This number when squared or multiplied by itself results in the original number n. The square root of 77 can be represented in the following ways.

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

• 77 is not a perfect square, which means that it does not have a natural number as its square root.
• Square root of 77 in the decimal form is √77 = 8.77496
• Square root of 77 cannot be expressed as a fraction of the form p/q. This indicates that the square root of 77 is an irrational number.

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

• Long Division Method
• Prime 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 pair up the digits 77 by placing a bar above 77. We will also pair the 0s in the decimal from left to right.
• Step 2: Find a number that, when multiplied to itself, gives a product less than or equal to 77. The number 8 fits here as 8 square gives 64. Dividing 77 by 8 with quotient as 8, we get the remainder as 13.
• Step 3: Drag a pair of 0’s down and place them next to 13 to make the dividend 1300.
• Step 4: Double the divisor 8, and enter 16 below with a blank digit on its right. Think of a number which is greater than or equal to the dividend, i.e., 1300. 167 is the perfect number to divide 1300.
• Step 5: Multiply 167 by 7 (167 × 7 = 1169 < 1300) and write the remainder, i.e. 131. 
• Step 6: Repeat this process until you get the desired number.

Therefore, the square root of 77 = 8.77

Prime Factorization Method

• To find the square root of 77, we will first express it in terms of its prime factors.
  Prime factorization of 77 = 7 × 11 
• Since all the prime factors of 77 are unique, none of these factors are perfect squares. The square root of 77 cannot be simplified.
• Prime factorization of 77 = 7 × 11
  Square root of 7 is √7 = 2.645
  Square root of 11 is √11 = 3.3166
• Therefore, the square root of √77 = 8.77

Explore square roots using illustrations and interactive examples

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• What is the negative root of 7700?
• Find the square root of 7700 up to 5 decimal places.
• What is the square root of:
  a) 770
  b) 777