## Square & Square Root of 100

## Square of 100

**100² (100×100) = 10000**

The square number of 100 is calculated by multiplying the number by itself. Specifically, 100 multiplied by 100 equals 10,000. This operation is fundamental in mathematics, especially in algebra.

## Square Root of 100

**√100 = 10**

The square root of a number In mathematical notation, the square root of 100 is expressed as

√100.

The square root of 100 is 10. This is because 10 multiplied by itself (10 × 10) equals 100. Mathematically, the concept of a square root arises from the function f(x)=x ² , where finding the square root of a number means determining the non-negative value x such that f(x)=100.

**Square Root of 100:** 10

**Exponential Form: **100^1/2 or 100^0.5

**Radical Form:** √100

## Is the Square Root of 100 Rational or Irrational?

This is because it can be expressed as an exact fraction. Specifically, the square root of 100 is 10, which can be expressed as the fraction 10/1. In general, a number is considered rational if it can be expressed as a fraction where both the numerator and the denominator are integers (and the denominator is not zero).

rational numbers As you mentioned, rational numbers are numbers that can be expressed as a fraction where both the numerator and the denominator are integers, and the denominator is not zero. This includes**Example:**1/2,3/4

Irrational numbers, on the other hand, cannot be expressed as a ratio of two integers. Their decimal expansions are infinite and non-repeating. These numbers often arise in geometry and algebra, especially involving roots of numbers that are not perfect squares or certain ratios like the circumference to the diameter of a circle (π).

**Example:**√2,√3

## Methods to Find Value of Root 100

### 1. Guess and Check Method

This method involves guessing numbers that might be the square root and then squaring them to see if the result is 100. For example:

- Guess 10. 10×10=100. The guess is correct.

### 2. Prime Factorization

This involves breaking down the number into its prime factors:

- The prime factors of 100 are 2²×5².
- To find the square root, take one factor from each pair of identical factors: 2×5=10.

### 3. Using a Calculator

Simply using a scientific calculator, you can find the square root function (often denoted as ) and input 100 to get the result.

### 4. Long Division Method

This is a traditional approach similar to long division:

- Pair the digits of 100 from right to left (in this case, you have 100).
- Estimate a factor (for 100, start with 10 because 10² is 100).
- Divide 100 by this estimate, adjust the estimate, and continue until the estimate does not change, confirming that 10 is the square root.

### 5. Exponentiation and Logarithms

Using properties of logarithms or exponents:

- If
*x*²=100, then taking logarithms of both sides (say, natural log or log base 10), you have 2log*x*=log100. - Solve for
*x*by finding log100 (which is 2 if using log base 10) and then log*x*=1, leading to*x*=10¹=10.

## Square Root of 100 by Long Division Method

**Step 1: Pair the digits from right to left.**

For the number 100, pair the digits as 1 and 00, with a bar over them to indicate the pairing.

**Step 2: Find the largest number whose square is less than or equal to the first pair.**

For the first pair (1), the largest number whose square is less than or equal to 1 is 1 itself (since 1×1=1). Subtract 1 from 1, which leaves a remainder of 0. Write down 1 as part of the quotient.

**Step 3: Bring down the next pair of digits next to the remainder.**

Bring down 00 to the remainder, making it 00. Now, double the quotient (which is currently 1) to get 2. This 2 becomes the first digit of your new divisor.

**Step 4: Complete the division to find the next digit of the quotient.**

Find a digit to place in the unit’s place of the new divisor (currently 20_) so that its product with the same digit is less than or equal to 00. Placing 0 in the unit’s place makes the new divisor 20. 20×0=0, which fits since it leaves a remainder of 0.

## Is 100 Perfect Square root or Not

Yes, 100 is a perfect square. This means there is a whole number (in this case, 10) that can be multiplied by itself to give the number 100. Thus, 10×10=100, confirming that 100 is indeed a perfect square.

## FAQ’S

## How to solve √ 100?

To solve √100, you can simply recognize that the number 100 is a perfect square. The square of 10 is 100, hence, √100=10.

## What is 100 a perfect square?

Yes, 100 is a perfect square. A number is considered a perfect square if there is an integer that can be multiplied by itself to reach that number. In the case of 100, it is 10×10, which makes it a perfect square.

## What is the principal square root of √ 100?

The principal square root of a number refers to the non-negative square root. For 100, the principal square root is 10. This is typically denoted as √100=10, emphasizing that it’s the positive square root.