Square Root Of 16 Simplified: Explanation And Solution

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Introduction

As a professional teacher, one of the most common questions I get from my students is about simplifying square roots. In this article, we will discuss how to simplify the square root of 16 and provide a step-by-step solution to the problem.

What is a Square Root?

A square root is a number that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3 because 3 x 3 = 9. The symbol used for square root is √.

What is the Square Root of 16?

The square root of 16 is a number that, when multiplied by itself, gives 16. In other words, the square root of 16 is 4 because 4 x 4 = 16.

How to Simplify the Square Root of 16?

To simplify the square root of 16, we need to factor the number inside the square root sign into its prime factors. 16 can be factored as 2 x 2 x 2 x 2 or 2^4. We can then take out the pair of 2s outside the square root sign and simplify it to 2 times the square root of 2.

Step-by-Step Solution

1. Write the square root of 16 as √16. 2. Factor 16 into its prime factors: 2 x 2 x 2 x 2 or 2^4. 3. Take out the pair of 2s outside the square root sign: 2 x √(2^2). 4. Simplify 2 x 2 to get 4: 4√2. 5. The simplified form of the square root of 16 is 4√2.

Why Simplify Square Roots?

Simplifying square roots makes it easier to perform arithmetic operations such as addition, subtraction, multiplication, and division. It also helps to identify irrational numbers, which are numbers that cannot be expressed as a ratio of two integers, unlike rational numbers.

Examples of Simplifying Square Roots

Let's look at some examples of simplifying square roots: 1. Simplify √25. 25 can be factored as 5 x 5. √25 = √(5 x 5) = 5. 2. Simplify √50. 50 can be factored as 2 x 5 x 5. √50 = √(2 x 5 x 5) = 5√2. 3. Simplify √72. 72 can be factored as 2 x 2 x 2 x 3 x 3. √72 = √(2 x 2 x 2 x 3 x 3) = 6√2.

Conclusion

Simplifying square roots is an essential skill in mathematics. In this article, we have discussed how to simplify the square root of 16 and provided a step-by-step solution to the problem. We have also explained why simplifying square roots is important and provided some examples of simplifying square roots. By mastering this skill, you can make your calculations easier and more efficient.