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Chapter 1: Problem 667

Simplify. $$ -\sqrt{4} $$

Short Answer

Expert verified
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Step by step solution

01

Identify the Square Root

Start by identifying the square root expression. The expression inside the square root is 4.
02

Calculate the Square Root

Calculate the square root of 4. Since \(\text{4}\text{ is a perfect square }\rightarrow \(\text{2}^2 = 4\)\)), \( \sqrt{4} = 2 \).
03

Apply the Negative Sign

Apply the negative sign outside the square root to the result. Since we found \( \sqrt{4} = 2 \), then \( -\sqrt{4} = -2 \).

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Key Concepts

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

Square roots
Square roots are special numbers. They help us find a number which, when multiplied by itself, gives the original number. For example, in the exercise given, we want to simplify \(-\sqrt{4}\). Let's look inside the square root first. We have 4 here. Do you remember what the square root of 4 is? It is 2! Because 2 multiplied by 2 gives us 4. So, we have \(\sqrt{4} = 2\). After that, to find the final answer, we just need to think about the negative sign in front of the square root. This will make our result negative too.
Negative numbers
Negative numbers might seem tricky at first, but they are just numbers less than zero. In our exercise, we start with a square root and come up with 2. Then, the negative sign outside \(-\sqrt{4}\) means we must change our result to a negative number. So, our 2 becomes -2. That's all it takes to handle negative numbers in this context!
Remember:
  • Negative numbers are important when dealing with square roots.
  • They change the sign of the final result to negative.
Perfect squares
Perfect squares are numbers that come from squaring whole numbers. This means you multiply a whole number by itself. In our exercise, 4 is what we call a perfect square. This is because \(2^2 = 4\). Knowing your perfect squares can make solving these exercises a lot easier. Here are some common perfect squares to remember:
  • 1 (since \(1^2 = 1\))
  • 4 (since \(2^2 = 4\))
  • 9 (since \(3^2 = 9\))
  • 16 (since \(4^2 = 16\))

Keep practicing identifying perfect squares. It will help you simplify square roots more quickly. In summary, if the number inside the square root is a perfect square, the solution gets easier.

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Most popular questions from this chapter

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Adele's shampoo sells for $$\$ 3.99\( per bottle at the grocery store. At the warehouse store, the same shampoo is sold as a 3 pack for \)\$ 10.49 .\( To find the cost of 3 bottles at \)\$ 3.99,\( notice that 3.99 is \)4-0.01\( (a) Multiply 3(3.99) by using the distributive property to multiply \)3(4-0.01)$$. (b) How much would Adele save by buying 3 bottles at the warehouse store instead of at the grocery store?

Explain how you can multiply \(4(\$ 5.97)\) without paper or calculator by thinking of \(\$ 5.97\) as \(6-0.03\) and then using the distributive property.
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