## Square & Square Root of 121

## Square of 121

**121²(121×121) = 14641**

The square number of 121 is calculated by multiplying the number by itself, which is mathematically represented as 121². This arithmetic operation results in a total of 14641. Squaring a number is a fundamental mathematical concept that involves raising the number to the power of two, yielding its square.

## Square Root o f 121

**√121 = 11**

The square root of 121 is exactly 11, as 11 multiplied by itself equals 121. This integer result distinguishes it from the square root of 128, which is not a whole number. In various mathematical applications, the precise value of √121, 11, is utilized for its simplicity and accuracy in calculations involving area, distance, and more.

**Square Root of 128: **11

**Exponential Form: **121^1/2 or 121^0.5

**Radical Form: **√121

## Is the Square Root of 121 Rational or Irrational?

The square root of 121 is rational because it equals 11, which is a whole number. Rational numbers are those that can be expressed as the quotient of two integers, and since 11 can be written as 11/1, it fits this definition.

Rational numbers are numbers that can be expressed as a fraction, where the numerator and denominator are both integers, and the denominator is not zero. In other words, a rational number can be written in the form a/b, where “a” and “b” are integers, and “b” is not equal to zero. Rational numbers include integers, fractions, and terminating or repeating decimals.

**Examples: **2/3,5/4

Irrational numbers are numbers that cannot be expressed as a fraction of two integers and are non-terminating and non-repeating decimals. In simpler terms, these numbers cannot be written as a ratio of two integers. Instead, they go on forever without repeating a pattern.

**Examples: **√2,(π)

## Methods to Find Value of Root 121

**Prime Factorization:**Breaking down 121 into its prime factors (11 * 11), then pairing them up to find the square root (11).**Long Division:**Using a long division method specifically designed for finding square roots, although this may be less common for smaller numbers like 121.**Using a Calculator:**Entering √121 into a calculator or a mathematical software yields the result directly.**Estimation:**Recognizing that 121 falls between the squares of 10 (100) and 11 (121), one can estimate the square root to be close to 11.

## Square Root of 121 by Long Division Method

**Step 1:** Pair up the digits by putting a bar above them.

**Step 2: **Start with a divisor. Since 1*1 = 1 ≤ 12, the divisor is 1. The quotient is 1, and the remainder is 0.

** Step 3: **Double the divisor, making it 2. Then, guess a digit to fill in the blank such that when it’s multiplied by the new divisor and added to the previous result, it’s less than or equal to 12. The largest digit that fits is 1. Thus, the quotient becomes 11, and the remainder is 0.So, the square root of 121 is 11.

## Is 121 Perfect Square root or Not

Yes, because its Perfect square root is a whole number, namely 11. In mathematics, a perfect square is a number that can be expressed as the product of an integer multiplied by itself. Therefore, 121 qualifies as a perfect square due to the exactness of its square root.

## FAQ’S

## What are the two roots of 121?

The two roots of 121 are both real and equal, and they are 11 and -11. In other words, when 11 is squared, it equals 121, and similarly, when -11 is squared, it also equals 121. These roots represent the solutions to the equation x^2 = 121.

## What are the factors of 121?

The factors of 121 are the numbers that can evenly divide 121 without leaving a remainder. In this case, the factors of 121 are 1, 11, and 121. When multiplied together, 1 * 11 * 11 = 121. These are the only combinations of factors that result in 121, making them its complete set of factors.

## What goes into 121 evenly?

To determine what goes into 121 evenly, we look for numbers that divide 121 without leaving a remainder. In this case, the numbers 1, 11, and 121 go into 121 evenly. When divided by 1, 11, or 121, there is no remainder, indicating that they are factors of 121. Therefore, 121 can be evenly divided by 1, 11, and 121.

## What times 11 equals 121?

11 times 11 equals 121. This multiplication is represented as 11 * 11 = 121. It shows that when the number 11 is multiplied by itself, the result is 121. This relationship demonstrates the square of 11, which is 121.