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Chapter 1: Problem 19

Evaluate each radical. $$\sqrt{49}$$

Short Answer

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Step by step solution

01

Identify the Radical Expression

The given expression is \(\textstyle \sqrt{49} \).
02

Find the Square Root

To evaluate \( \textstyle \sqrt{49} \), determine which number multiplied by itself gives 49.
03

Perform the Calculation

Since \( \textstyle 7 \times 7 = 49 \), we conclude that \( \textstyle \sqrt{49} = 7 \).

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Key Concepts

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

Radical Expressions
A radical expression involves a root. For example, a square root or cube root of a number. The symbol for a square root is \( \sqrt{} \). This symbol tells us that we need to find the number which, when multiplied by itself, equals the number inside the radical.

When dealing with radical expressions:
  • The number inside the radical is called the radicand.
  • The square root is the most common radical, but there are also cube roots and higher-order roots.
Radicals can appear simple, but they require proper understanding to work with them correctly. In our exercise, the given radical expression is \( \sqrt{49} \).
Square Roots
The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3, because \( 3 \times 3 = 9 \). This is represented as \( \sqrt{9} = 3 \).

To find the square root, ask: 'What number times itself equals the radicand?' In our exercise:
  • We have \( \sqrt{49} \).
  • We need to find a number which when multiplied by itself gives 49.
  • We observe that \( 7 \times 7 = 49 \) so the answer is 7.
Hence, \( \sqrt{49} = 7 \). Understanding this helps in evaluating other square roots efficiently.
Basic Arithmetic
Basic arithmetic includes addition, subtraction, multiplication, and division. When dealing with square roots, multiplication is key. You need to know which numbers multiply together to form the radicand.

Steps:
  • Identify the number inside the square root (radicand).
  • Determine a number that multiplies by itself to give that radicand.
Example review:
  • Radicand: 49
  • Number: 7, because \( 7 \times 7 = 49 \)
  • Thus, \( \sqrt{49} = 7 \)
Grasping multiplication in basic arithmetic makes understanding square roots and radicals straightforward.

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