Square Root Of 6 Explained With Value And Method

The square root is a topic that many students find difficult to understand. However, once you understand the concept well, finding square roots will no longer be a challenge for you. So, in simple words square root, in mathematics, is a factor of a number that, when multiplied by itself, gives the original number. For example, both 3 and –3 are square roots of 9.

The square root of a number a is the number b such that b² = a. The square root of any number is represented by the symbol and is also often known as radical. The number or expression given under the square root symbol is known as radicand. The square root is a commonly used function in Mathematics. It is widely used in subjects like Mathematics and Physics. Sometimes it is tedious to find the square root of a number, especially the numbers which are not the perfect square of the number. In this article, we will discuss the square root of 6, and how to calculate the root 6 value using the simplifying square root method.

What is the root 6 value?

The root 6 value is 2.449

Square Root of 6 Definition

The square root of a number 6 is a number y such that y² = 6. The square root of 6 in radical form is written as √6. The square root of 6 in radical form is expressed as√6

How to Calculate the Under Root 6 Value?

We can calculate the under root 6 value using different methods of square roots. These methods can be the long division methods, prime factorization method, or simplifying square root method. Let us discuss how to calculate the under root 6 value using the simplifying square root method.

To simplify a square root, make the number under the square root as small as possible while keeping it as a whole number. Mathematically, it can be expressed as: √x.y=√x×√y

To express the square root of 6 in the simplest form, we will make the number 6 as small as possible, ensuring to keep it as a whole number. Hence, the square root of 6 in simplest form is represented as√6=√2×√3. This can be further simplified by substituting the value of √2 and √3

\[\sqrt{6}=\sqrt{2}\times \sqrt{3}\]

\[\sqrt{6}=1.414\times 1.732\]

\[\sqrt{6}=2.449\]

Hence, the square root of 6 in simplest form is 2.449.  Similarly, we can also calculate the square root of any other whole numbers and their factors. Hence, simplifying the square root method is the simplest method of calculating the square root. We can also calculate the value of under root 6 using the calculator as this will give us the exact value. The exact value of the square root will always be given in a decimal number as it is impossible to determine a positive whole integer as a root for non-rational numbers.

Simplifying the Square Root Using Perfect Square Method

Following are the steps to simplify the square root using the perfect square method:

1. Find the perfect square that divides the number in the radicand.

2. Express the numbers as a factor of a perfect square.

3. Simplify the radicals.

Solved Example

1. Simplify $\mathbf{\sqrt{300}}$

Solution:

\[\sqrt{300}=\sqrt{100\times 3}\]

\[\sqrt{300}=\sqrt{10\times 10\times 3}\]

\[\sqrt{300}=10\sqrt{3}\]

Hence,\[\sqrt{300}\] can be simplified as \[10\sqrt{3}\]

2. Simplify the following radical expressions :

1. \[\sqrt{48}\]

2. \[\sqrt{75}\]

Solutions:

i.$\mathbf{\sqrt{48}}$

Step 1: The perfect square 16 will divide the number 48.

Step 2: Express 48 as a factor of 16

48=16×3

Step 3: Reduce the square root of 16 as shown below:

\[\sqrt{48}=\sqrt{16\times 3}\]

\[\sqrt{48}=\sqrt{4\times 4\times 3}\]

\[\sqrt{48}=4\sqrt{3}\]

Hence,\[\sqrt{48}\] can be simplified as\[4\sqrt{3}\]

ii.$\mathbf{\sqrt{75}}$

Step 1: The perfect square 25 will divide the number 75.

Step 2: Express 75 as a factor of 25.

75=25×3

Step 3: Simplify the radicals as shown below: 

\[\sqrt{75}=\sqrt{25\times 3}\]

\[\sqrt{75}=\sqrt{5\times 5\times 3}\]

\[\sqrt{75}=5\sqrt{3}\]

Hence,\[\sqrt{75}\] can be simplified as\[5\sqrt{3}\]