## Square & Square root of 1

## Square of 1

**1² (1×1) = 1**

To calculate the square of **1**, you simply multiply **1 **by itself:

Therefore, the square of 1 is 1. This straightforward calculation is a building block for more complex mathematical operations and concepts, including algebraic equations, geometric formulas, and statistical models.

## Square Root of 1

**√1 = 1.0**

The square root of 1 is simply 1. This is because the square root operation asks the question, “What number, when multiplied by itself, gives the original number?” For the case of 1, multiplying 1 by itself (1 × 1) yields 1. Mathematically, this is expressed as 1=11=1. The concept is straightforward and serves as a fundamental example of how square roots work, illustrating that the square root of a positive number can be positive (and in this unique case, the same as the original number).

**Square Root of 1 :**1.0

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

**Radical Form:** √1

## Is the Square Root of 1 Rational or Irrational?

**The square root of 1 is rational**

- A
**rational number**is any number that can be expressed as a fraction a/b where a and b are integers, and b is not equal to zero. It includes integers, fractions, and finite or repeating decimals. - An
**irrational number**is a number that cannot be expressed as a simple fraction. Irrational numbers have non-repeating, non-terminating decimal expansions.

A rational number is defined as a number that can be expressed as the fraction **a/b** where ** a **and

**are integers, and**

*b**b*is not zero. The square root of

**1**is exactly

**1 (√1=1**), which can be expressed as a fraction like

**1/1**, fitting the definition of a rational number perfectly.

## Methods to Find Value of Root 1

To find the value of the square root of 1 (√1) , you can follow this straightforward approach:

**Understand what square root means**: The square root of a number is a value that, when multiplied by itself, gives the original number.**Apply this to 1**: Ask yourself, “What number times itself equals 1?” The answer is simple: 1, because 1×1=1.

## Square Root of 1 by Long Division Method

**Square Root of 1 (√1):**

**Recognize the operation:** Understand that finding the square root of a number involves determining the number that, when multiplied by itself, equals the original number.

**Compute:** Calculate the square root of 1. Since 1×1 = 1, the square root of 1 is 1.

**Interpretation:** This means that the length of each side of a square with an area of 1 square unit is 1 unit.

**Check:** Verify the result by squaring the calculated square root. In this case, 1×1 = 1, confirming that the square root of 1 is indeed 1.

## 1 is Perfect Square root or Not

**Yes, 1 is a perfect square**

The square root of 1 is 1, because 1×1=1. A perfect square is a number that can be expressed as the product of an integer with itself.

## FAQ’S

## What is the square root of a negative 1?

The square root of negative 1 is defined as “i”, where “i” is the imaginary unit. It satisfies the equation i² = -1, a foundational concept in complex numbers.

## Can √ 1 be a value?

Yes, √1 can be a value. The square root of 1 is 1, because 1 squared (1×1) equals 1. It satisfies the definition of a square root.

## Why is √ 1 imaginary?

√1 is not imaginary; it is real and equals 1. The confusion might arise with √-1, which is imaginary, denoted as i, defining the basis for complex numbers.