The square root of 121 is expressed as √121 in the radical form and as (121)½ or (121)0.5 in the exponent form. The square root of 121 is 11. It is the positive solution of the equation x2 = 121. The number 121 is a perfect square.

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Square Root of 121: 11Square Root of 121 in exponential form: (121)½ or (121)0.5Square Root of 121 in radical form: √121
 1 What Is the Square Root of 121? 2 Is Square Root of 121 Rational or Irrational? 3 How to Find the Square Root of 121? 4 FAQs on Square Root of 121

We know that addition has an inverse operation in subtraction and multiplication has an inverse operation in the division. Similarly, finding the square root is an inverse operation of squaring. The square root of 121 is the number that gets multiplied to itself to give the number 121.

A rational number is a number that can be expressed in the form of p/q, where p and q are integers and q is not equal to 0. We already found that 121 = 11. The number 11 is a rational number. So, the square root of 121 is a rational number.

## How to Find the Square Root of 121?

We will discuss two methods of finding the square root of 121

Prime FactorizationLong division

### Square Root of 121 By Prime Factorization

Prime factorization is a way of expressing a number as a product of its prime factors. The prime factorization of 121 is 121 = 11 × 11 = 112. To find the square root of 121, we take one number from each pair of the same numbers and we multiply them.

121 = 11 × 11 121 = 11

### Square Root of 121 By Long Division

The value of the square root of 121 by long division method consists of the following steps:

Step 1: Starting from the right, we will pair up the digits by putting a bar above them.Step 2: Find a number which, when multiplied to itself, gives the product less than or equal to 1. So, the number is 1. Putting the divisor as 1, we get the quotient as 1 and the remainder 0Step 3: Double the divisor and enter it with a blank on its right. Guess the largest possible digit to fill the blank which will also become the new digit in the quotient, such that when the new divisor is multiplied to the new quotient the product is less than or equal to the dividend. Divide and write the remainder.

See more: The Second Number In An Ordered Pair, What Is The Second Number Of An Ordered Pair

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Important Notes:

The square root is the inverse operation of squaring.We can find the square root of 121 using prime factorization, repeated subtraction, and the long division method.The square root of a number is both negative and positive for the same numerical value i.e., the square root of 121 will be 11.

Think Tank:

We know that (-11) × (-11) =121. So, can we say that -11 is a square root of 121?Can you determine a quadratic equation whose roots are 121 and -121?