Problem 50 Find each square root. If it is ... [FREE SOLUTION]

Chapter 0: Problem 50

Find each square root. If it is not a real number, say so. $$ -\sqrt{0.64} $$

Short Answer

Expert verified

-0.8

Step by step solution

Understand the Square Root Operation

The square root of a number $ x $ is a value $ y $ such that $ y^2 = x $. In this case, we need to find $ \sqrt{0.64} $.

Compute the Square Root

Calculate the square root of 0.64: \[ \sqrt{0.64} = 0.8 \] because $ (0.8)^2 = 0.64 $.

Consider the Negative Sign

The problem asks for $ -\sqrt{0.64} $. Since we've found $ \sqrt{0.64} = 0.8 $, we multiply by -1: \[ -\sqrt{0.64} = -0.8 \].

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Understanding Square Roots

Square roots are essential in algebra and understanding them can help you solve a variety of problems more easily.

The square root of a number is a value that, when multiplied by itself, gives the original number. Let's call the original number $ x $. If $ y $ is the square root of $ x $, then $ y^2 = x $.

In our exercise, we have $ \sqrt{0.64} $. To find this value, we need to figure out what number multiplied by itself equals 0.64.

For example, if $ y = 0.8 $, then $ (0.8)^2 = 0.64 $.

So, $ 0.8 $ is the square root of 0.64.

Negative Square Roots

Negative square roots might seem confusing at first, but they are quite straightforward once you get the hang of it.

If we take the square root of a positive number, we usually consider the positive value. For instance, $ \sqrt{0.64} = 0.8 $.

But what if we are asked for the negative square root? Simply put, we multiply the positive square root by -1.

In our exercise, we have to find the negative square root of 0.64:

First, we compute $ \sqrt{0.64} = 0.8 $.
Second, we apply the negative sign: $ -\sqrt{0.64} = -0.8 $.

Real Numbers

Real numbers include all the numbers you will typically encounter, such as whole numbers, fractions, and decimals.

They can be positive, negative, or zero. Real numbers are represented on the number line and are pretty much everywhere in algebra.

When dealing with square roots, it鈥檚 important to understand that:

The square root of a real number is also a real number if the original number is non-negative.
If we are dealing with negative numbers, like $ -\sqrt{0.64} $, we are still in the realm of real numbers.

By understanding real numbers, you鈥檒l have a solid foundation to tackle problems involving square roots.

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91影视

Find each square root. If it is not a real number, say so. $$ -\sqrt{0.64} $$

Short Answer

Step by step solution

Understand the Square Root Operation

Compute the Square Root

Consider the Negative Sign

Key Concepts

Understanding Square Roots

Negative Square Roots

Real Numbers

One App. One Place for Learning.

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