What is the square root of 0.16?

The square root of 0.16 is 0.4. To understand how we arrive at this answer, let’s break it down step by step.

Understanding Square Roots

A square root of a number is a value that, when multiplied by itself, gives the original number. In mathematical terms, if \( x \) is the square root of \( y \), then \( x^2 = y \). For example, if we take the square root of 0.16, we are looking for a number that, when squared, equals 0.16.

Calculating the Square Root

To find the square root of 0.16, we can think of it in terms of fractions. The number 0.16 can be expressed as:

• 0.16 = 16/100

Now, we can simplify this fraction:

• 16/100 = (4/10)^2

Here, we see that \( 4/10 \) is the square root of \( 16/100 \). Simplifying \( 4/10 \) gives us 0.4. Therefore, the square root of 0.16 is 0.4.

Verification

To verify our answer, we can square 0.4 and check if we get back to 0.16:

• 0.4 × 0.4 = 0.16

This confirms that our calculation is correct. Thus, the square root of 0.16 is indeed 0.4.

Practical Applications

Understanding square roots is useful in various fields, such as geometry, physics, and finance. For example, in geometry, the square root can help determine the length of a side of a square when you know its area. If the area is 0.16 square units, the length of each side would be 0.4 units.

In summary, the square root of 0.16 is 0.4, and this concept plays a significant role in many mathematical applications. If you have any more questions about square roots or related topics, feel free to ask!