## Square & Square Root of 4900

In the realm of mathematics, particularly within algebra, the significance of squares and square roots cannot be overstated. These concepts form the bedrock upon which our understanding of rational and irrational numbers is built. By taking a number like 4900 and squaring it, we illustrate the fundamental nature of this operation, paving the way for deeper exploration of mathematical relationships and patterns.

## Square of 4900

**4900² (4900 × 4900) = 24,010,000**

A square number such as 4900 arises from multiplying an integer by itself. The square of 4900 equals 24,010,000, highlighting algebraic principles and enriching comprehension of mathematical relationships and patterns within algebraic studies and beyond.

## Square Root of 4900

**√4900 = 70**

The square root of 4900, a perfect square number, is 70. Mastery of square roots involves identifying the number that, when multiplied by itself, equals 4900. This understanding is crucial for exploring algebraic relationships and patterns within mathematics.

**Square Root of 4900**: 70

**Exponential Form**: 4900^½ or 4900^0.5

**Radical Form:** √4900

## Is the Square Root of 4900 Rational or Irrational?

**The square root of 4900 is rational.**

Rational Numbers: Rational numbers are expressible as fractions of two integers.

Irrational Numbers: Irrational numbers cannot be expressed as fractions of integers.

As the square root of 4900 is a perfect square, it is rational. It can be expressed as the fraction 70/1.

## Methods to Find the Value of Root 4900

**Estimation Method:** Begin with an initial approximation and refine it iteratively using methods like Newton-Raphson.

**Prime Factorization Method:** Express 4900 as a product of prime factors, then find the square root of each prime factor.

**Calculator:** Utilize a calculator with a square root function to directly compute the square root of 4900.

## Square Root of 4900 by Long Division Method

**Forming pairs:** 49 and 00

**Step 1:**

Find a number Y (7) whose square is ≤ 49. Now divide 49 by 7 with the quotient as 7.

**Step 2:**

Bring down the next pair 00 to the right of the remainder 0. The new dividend is now 00.

**Step 3:**

Add the last digit of the quotient (7) to the divisor (7), resulting in 14. To the right of 14, find a digit Z (which is 0) such that 14Z × Z ≤ 00. After finding Z, together 14 and Z (0) form a new divisor, 140, for the new dividend 00.

**Step 4:**

Divide 00 by 140 with the quotient as 0, giving the remainder as 0 – 140 × 0 = 0 – 0 = 0.

**Conclusion:**

We stop the process since the remainder is now 0 and there are no more digits that can be brought down. Therefore, the square root of 4900 by the long division method is 70.

## 4900 is a Perfect Square or Not

**Yes, 4900 is a perfect square number.**

4900 is a perfect square because it can be expressed as the product of an integer multiplied by itself. In this case, 70 × 70 = 4900, indicating that 4900 is indeed a perfect square.

## FAQs

## What is the prime factorization of 4900?

The prime factorization of 4900 is 2²× 5²× 7²

## What is the significance of the square root of 4900 in geometry?

In geometry, the square root of 4900 (70) represents the length of the side of a square with an area of 4900 square units.

## Can the square root of 4900 be simplified further?

No, the square root of 4900 cannot be simplified further as it is already in its simplest form.

## What are the factors of 4900?

The factors of 4900 are all numbers that divide evenly into 4900, including 1, 2, 4, 5, 7, 10, 14, 20, 25, 35, 49, 50, 70, 98, 100, 140, 196, 245, 350, 490, 700, 980, 1225, 2450, and 4900.