Problem 295 - Intermediate Algebra

Question

In the following exercises, simplify. $$ -\sqrt{100} $$

Step-by-Step Solution

Answer

-10

Step 1: Identify the square root

First, find the square root of the number inside the square root symbol. We have \(\sqrt{100}\), and we know that \(\sqrt{100} = 10\).

Step 2: Apply the negative sign

Since the original expression has a negative sign in front of the square root, we need to apply it to the result from Step 1. Therefore, \(-\sqrt{100} = -10\).

Key Concepts

square root

A square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 100 is 10 because \(10 \times 10 = 100\). Square roots are often written with the radical symbol \(\sqrt{}\), followed by the number you want to find the root of.
In our exercise, the number under the square root symbol is 100: \(-\sqrt{100}\).
To simplify it, we first need to find the square root of 100.

negative sign

When we see a negative sign in front of a square root, it means that the answer will be negative. In mathematics, the negative sign changes the value from positive to negative. For example, if \(- \sqrt{100}\) gives us -10, that's because the negative sign is applied to the positive result (10) of the square root of 100.
The key is to first find the square root, then apply the negative sign. This ensures we correctly understand the order of operations.
In our example, \(\sqrt{100} = 10\), and then applying the negative sign, \(-10\).

simplification steps

Simplifying square roots is a process that involves a few clear steps. Here's a step-by-step guide you can follow to make things easier:

• Identify the square root of the number inside the radical symbol (\(\sqrt{}\)). For instance, with \(- \sqrt{100}\), the number inside is 100.


• Find the square root of this number. In our case, \(\sqrt{100} = 10\).


• Apply any additional operations, such as a negative sign. Since the original problem is \(-\sqrt{100}\), we take our result from the previous step, 10, and then apply the negative sign: \(-10\).

Following these steps ensures you can simplify square roots correctly every time.