/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 20 Simplify. $$ \sqrt{25}+\sqrt... [FREE SOLUTION] | 91影视

91影视

Log out

Learning Materials

Features

Discover

Chapter 9: Problem 20

Simplify. $$ \sqrt{25}+\sqrt{144} $$

Short Answer

Expert verified
17

Step by step solution

01

Calculate the square root of 25

To simplify the expression, calculate the square root of 25. The square root of 25 is 5, because \(\text{5} \times \text{5} = \text{25}\).
02

Calculate the square root of 144

Next, calculate the square root of 144. The square root of 144 is 12, because \(\text{12} \times \text{12} = \text{144}\).
03

Add the results of the square roots

Now, add the results from Step 1 and Step 2. \(5 + 12 = 17\).

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Over 30 million students worldwide already upgrade their learning with 91影视!

Key Concepts

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

square root calculation
To simplify expressions like \(\text{\sqrt{25} + \sqrt{144}}\), we need to understand how to calculate square roots.
A square root of a number is a value that, when multiplied by itself, gives the original number.

For example, the square root of 25 is 5, because:
\[5 \times 5 = 25\]
Similarly, the square root of 144 is 12, because:
\[12 \times 12 = 144\]
Always remember, square roots have two values, positive and negative. But for simplification problems, we typically consider the positive value (called the principal square root).
To calculate square roots without a calculator, we can use methods like factorization, perfect square comparison, or estimation.
addition of square roots
Once you've calculated the square roots, the next step is to add them together.
In our example:
\(\text{\sqrt{25} = 5}\) and \(\text{\sqrt{144} = 12}\).
Adding these two results:
\[5 + 12 = 17\]
This means that the simplified form of \(\text{\sqrt{25} + \sqrt{144}}\) is 17.

It鈥檚 important to note that we can only add or subtract square roots directly if they have the same radicand (the number inside the square root). For example, \(\text{\sqrt{9} + \sqrt{16}}\) is straightforward, but \(\text{\sqrt{9} + \sqrt{10}}\) is not because the radicands (9 and 10) are different.
In such cases, the result remains in an unsimplified form.
basic algebra
Understanding square roots and their operations is a fundamental part of basic algebra.
Algebra often involves finding unknown values, and simplification of expressions helps make equations easier to solve.

Here are some key points to remember:
  • Always simplify square roots first before performing additional operations.
  • Familiarize yourself with perfect squares (1, 4, 9, 16, 25, etc.).
  • Use properties of square roots such as the product property \(\text{\sqrt{a} * \sqrt{b} = \sqrt{a*b}}\).
  • Ensure proper handling of like terms when adding or subtracting square roots.
By mastering these concepts, you will strengthen your algebra skills and be better prepared for more complex mathematical problems.

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

In the following exercises, solve. (a) \(\sqrt{u}+1=\sqrt{u+4}\) (b) \(\sqrt{n-5}+4=\sqrt{3 n+7}\)

In the following exercises, solve. (a) \(\sqrt{r-1}-r=-1\) (b) \(\sqrt{z+100}-z+10=0\)

In the following exercises, simplify and rationalize the denominator. $$ \frac{6}{\sqrt{7}} $$

In the following exercises, solve. \(\sqrt{4 m+2}+2=6\)

In the following exercises, solve. $$ \sqrt{3 u-2}=\sqrt{5 u+1} $$
See all solutions

Recommended explanations on Math Textbooks

Probability and Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Mechanics Maths

Read Explanation

Statistics

Read Explanation

Geometry

Read Explanation

Discrete Mathematics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.