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Chapter 9: Problem 5

$$ \sqrt{625} $$

Short Answer

Expert verified
The square root of 625 is 25.

Step by step solution

01

Identify the square root operation

Recognize that the given problem is asking for the square root of 625, which means finding a number that, when multiplied by itself, equals 625.
02

Recall perfect squares

Think about the perfect squares, which are numbers such as 1, 4, 9, 16, 25, and so on, up to the perfect squares you are familiar with. Remember that 625 is a perfect square.
03

Find the square root

Consider the perfect square closest to 625. Recalling the list, 25 squared is 625 because 25 * 25 = 625.
04

Write the square root

The square root of 625 is 25, because 25 is the number that when multiplied by itself equals 625.

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Key Concepts

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

Perfect Squares
A perfect square is a number that results from multiplying a whole number by itself. For instance, 1, 4, 9, 16, and 25 are all perfect squares. This means:
  • 1 = 1 * 1
  • 4 = 2 * 2
  • 9 = 3 * 3
  • 16 = 4 * 4
  • 25 = 5 * 5
Understanding perfect squares is key to solving square root problems. When dealing with square roots, we are essentially looking for the number that was squared to get the original number. For example, with 625, realizing it's a perfect square helps us quickly identify that 25 is the square root because:

25 * 25 = 625.
Multiplication
Multiplication is one of the basic mathematical operations where we combine groups of equal sizes. In the context of perfect squares and square roots, multiplication plays a critical role. When we say a number is multiplied by itself, we mean that the number is used two times in a multiplication statement:
For example:
  • 5 * 5 = 25
  • 25 * 25 = 625
Here, the multiplication of 25 by itself gives 625. This is useful when solving square roots because it helps to validate our results. If we know the square of a number, we can check our work.

Example: If we guessed 25 is the square root of 625, we verify by confirming 25 multiplied by itself equals 625.
Mathematical Operations
Mathematical operations include addition, subtraction, multiplication, and division. The square root operation is a reverse of squaring a number. To find the square root of a number, we try to determine what number squared will equal the original number.
Steps for solving a square root operation:
  • Recognize the square root symbol: \( \sqrt{} \)
  • Identify that you're asked to find a number which, when multiplied by itself, gives the original number.
  • Recall perfect squares and find which one matches the given number.
  • Verify the chosen number by multiplying it by itself.
In this case, \( \sqrt{625} \) asks us to find a number, which when squared, equals 625.

Recall that 25 * 25 gives us 625. Therefore, the square root of 625 is 25.

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