Understanding The Square Root Of 64Y16

Introduction

The square root of 64y16 is a mathematical expression that a lot of students find challenging to understand. However, it is not as complicated as it may seem. In this article, we will explain what the square root of 64y16 means and how to solve it.

What is a Square Root?

Before we delve into the square root of 64y16, it's essential to understand what a square root is. A square root is a number that, when multiplied by itself, gives the original number. For instance, the square root of 16 is 4 because 4 multiplied by 4 equals 16.

What is the Square Root of 64y16?

Now that we understand what a square root is let's move on to the main topic. The square root of 64y16 is a bit more complicated because it involves variables. However, we can simplify it by breaking it down into smaller parts.

Step 1: Break down 64y16

We can break down 64y16 into 64 and y16. Therefore, the square root of 64y16 is equal to the square root of 64 multiplied by the square root of y16.

Step 2: Solve the Square Root of 64

The square root of 64 is 8 because 8 multiplied by 8 equals 64.

Step 3: Solve the Square Root of y16

To solve the square root of y16, we need to look for a perfect square among the factors of y16. The factors of y16 are y and 16. 16 is a perfect square because 4 multiplied by 4 equals 16. Therefore, we can write y16 as y times 16.

Step 4: Simplify the Square Root of y16

Now that we know that y16 is equal to y times 16, we can simplify the square root of y16 as the square root of y times the square root of 16. The square root of 16 is 4, and the square root of y is the square root of y. Therefore, the square root of y16 is equal to 4 times the square root of y.

Final Solution

Now that we have solved the square root of 64 and the square root of y16, we can combine them to get the final solution. The square root of 64 is 8, and the square root of y16 is 4 times the square root of y. Therefore, the square root of 64y16 is 8 times 4 times the square root of y, which simplifies to 32√y.

Conclusion

The square root of 64y16 may seem complicated at first, but it is easy to solve once you break it down into smaller parts. Remember to always look for perfect squares when solving the square root of a variable. With practice, you'll be able to solve more complex square roots effortlessly.