# How to find the square root of 80?

Number System is a method of representing Numbers on the Number Line with the help of a set of Symbols and rules. These symbols range from 0-9 and are termed digits. Number System is used to perform mathematical computations ranging from great scientific calculations to calculations like counting the number of Toys for a Kid or Number chocolates remaining in the box.

### Square root

The Square root of a number is that value which when multiplied by itself will give its original number. The square root is represented with the symbol √ called as **radical or radix** followed by the number which is called radicand i.e., **√x**.

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**For example:**

√4 = 2

√9 = 3

√16 = 4

√25 = 5

**How to find **the **square root of 80 **

There are multiple ways to find the square root of 80, the square root of 80 (√80), or any other number can be found with the help of the following three methods,

- Estimation and Approximation
- Prime Factorization
- Long Division Method

**Estimation and Approximation :**

The number S is expressed as a * 10^{2n} in scientific notation and √S ≈ 6 * 10^{n }, if a >= 10

√80 ≈ 6, with an absolute error of 2.9

**Prime Factorization:**

**Step 1:**Find the prime factors of 80.

80 = (2 × 2 × 2 × 2 × 5)

**Step 2:**Pair similar factors.

√80 = √((2 × 2) × (2 × 2) × 5)

√80 = 2 × 2 × √(5)

√80 = 4√5 ≈ 8.94

**Long Division Method:**

**Step 1:**Try to make pairs of 2 digits. From right to left before the decimal point and left to right after decimal points.**Step 2:**Find a number**n**, such that when multiplied by itself given a number, which is less than or equal to 80. Here, n is 8 as 8 * 8 gives 64. Dividing 80 by 8, we get the quotient as 8 and the remainder as 16.**Step 3:**Drop the next pair down. Here, next is 00 and put it after the remainder of the previous operation which gives us 1600 as a new dividend.**Step 4:**Double the divisor of previous operations, i.e**n**which gives us 16, and find the largest possible digit(X) such that the quotient for which the product of 16X and X results in a value less than or equal to 1600.**Step 5:**Divide and write the remainder.**Step 6:**Repeat this process according to a given precision