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Chapter 9: Problem 4

Simplify. $$ \sqrt{169} $$

Short Answer

Expert verified
The square root of 169 is 13.

Step by step solution

01

Understand the Square Root Operation

The square root operation is used to find a number, which when multiplied by itself gives the original number. In this case, we are finding the square root of 169.
02

Find the Square Root of 169

Identify a number that when multiplied by itself results in 169. We know that 13 * 13 = 169.
03

Write the Result

Since the square root of 169 is 13, we can simplify \( \sqrt{169} \) as 13.

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Key Concepts

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

Square Root Operation
The square root operation is really important in math. It helps us find a number that, when multiplied by itself, gives us the original number.

For example, if we want to find the square root of 169, we need to ask ourselves: 'What number times itself equals 169?' This operation is essential in understanding how we can break down and simplify numbers.

The square root symbol is written as \( \sqrt{ } \). So, \( \sqrt{169} \) asks for the number which squared (multiplied by itself) equals 169.

Practice makes perfect with square roots. Try finding square roots of other numbers like \( \sqrt{4} \) or \( \sqrt{25} \) to get comfortable!
Simplification
Simplifying square roots can seem tricky at first, but it gets easier with practice.

Here are some steps to help you simplify square roots:
  • Identify the number you're finding the square root of.
  • Determine if this number is a perfect square (a number that can be expressed as another whole number times itself).
  • If it is not, find the largest perfect square factor and simplify accordingly.
Let's go through the steps using our example, \( \,\sqrt{169} \).

First, notice if 169 is a perfect square. Since we know that 13 * 13 = 169, we see that it is. This means \( \,\sqrt{169} = 13 \).

Simplifying square roots is easier when you recognize perfect squares quickly. Keep practicing!
Perfect Squares
Understanding perfect squares is vital for simplifying square roots.

A perfect square is a number that is the square of an integer. For example:
  • \(4\) is a perfect square because \(2 \, * \, 2 = 4\).
  • \(25\) is a perfect square because \(5 \, * \, 5 = 25\).
  • \(169\) is a perfect square because \(13 \, * \, 13 = 169\).
Recognizing these can save a lot of time. The more perfect squares you remember, the faster you can simplify square roots!

Try to memorize common perfect squares like \(1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169,\) and so on. This will make problems involving square roots much easier.

Keep practicing, and soon you'll be a pro at identifying and using perfect squares!

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Most popular questions from this chapter

In the following exercises, solve. \(\sqrt{6 s+4}=\sqrt{8 s-28}\)

In the following exercises, simplify by rationalizing the denominator. $$ \frac{\sqrt{5}}{\sqrt{y}-\sqrt{7}} $$

In the following exercises, check whether the given values are solutions. For the equation \(\sqrt{-y+20}=y:\) (a) Is \(y=4\) a solution? (b) Is \(y=-5\) a solution?

In the following exercises, simplify by rationalizing the denominator. (a) \(\frac{3}{3+\sqrt{11}}\) (b) \(\frac{8}{1-\sqrt{5}}\)

In the following exercises, simplify by rationalizing the denominator. $$ \frac{\sqrt{80 p^{3} q}}{\sqrt{5 p q^{5}}} $$
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