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Chapter 7: Problem 7

Simplify. Assume that variables represent positive real numbers. $$ -\sqrt{36} $$

Short Answer

Expert verified
The simplified expression is \(-6\).

Step by step solution

01

Understand the problem

The problem asks us to simplify the expression \(-\sqrt{36}\).The symbol \(-\) indicates a negative, and \(\sqrt{36}\) stands for the square root of 36.
02

Simplify the square root

Calculate the square root of 36. Since 36 is a perfect square,\(\sqrt{36} = 6\).
03

Apply the negative sign

Now, apply the negative sign in front of the square root result:\(-6\).This is the simplified form of the given expression.

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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 a fundamental idea in mathematics. When we talk about the square root of a number, we're looking for a value that, when multiplied by itself, gives us the original number.
Take for instance, the square root of 36. We ask: what number times itself equals 36? The answer is 6, because \(6 \times 6 = 36\).
When you see the symbol \(\sqrt{}\), it's asking you to find this special number. This process is very helpful when simplifying expressions. Knowing your perfect squares can make finding square roots quicker and easier.
Recognizing Perfect Squares
Perfect squares are numbers that have exact whole numbers as their square roots. Being familiar with perfect squares is invaluable when dealing with square roots. For example, numbers like 4, 9, 16, 25, 36, and 49 are a few early perfect squares.
  • 4 is a perfect square because \(2 \times 2 = 4\)
  • 9 is a perfect square because \(3 \times 3 = 9\)
  • 36 is a perfect square because \(6 \times 6 = 36\)
Knowing perfect squares speeds up the simplification of square roots since they directly result in whole numbers without the need for tricky calculations.
Handling Negative Numbers
Negative numbers can seem daunting at first, but they're straightforward once you break down what they mean. A negative sign basically indicates that a number is less than zero.
In the context of simplifying expressions, the negative sign in front of a square root means you're taking the opposite, or negating, the positive square root's result.
So, for \(-\sqrt{36}\), once you realize that \(\sqrt{36} = 6\), you simply apply the negative sign and say the simplified expression is \(-6\).
This step solidifies your understanding of both square roots and how negatives modify numbers.

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Most popular questions from this chapter

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