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Square roots of perfect squares

Learn how to find the square root of perfect squares like 25, 36, and 81.
Let's start by taking a look at an example evaluating the square root of 25:
25=?
Step 1: Ask, "What number squared equals 25?"
Step 2: Notice that 5 squared equals 25.
52=5×5=25
The answer
25=5
Here's a question to make sure you understood:
How can we be sure that 5 is the right answer?
Choose 1 answer:

Connection to a square

Finding the square root of 25 is the same as finding the side length of a square with an area of 25.
A square with unknown side lengths. The area is equal to 25.
A square with an area of 25 has a side length of 5.
A square with side legs of 5 units. The area is equal to 5 times 5, which is equal to 25.
A factor tree for 25. The number 25 is the product of 5 and 5. One of the number 5's is circled and the other is not.

Practice Set 1:

Problem 1A
42=
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

Reflection question

Which claim shows how square roots work?
Choose 1 answer:

Practice Set 2:

Problem 2A
1=
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

Practice Set 3:

Problem 3A
121=
  • Your answer should be
  • an integer, like 6
  • a simplified proper fraction, like 3/5
  • a simplified improper fraction, like 7/4
  • a mixed number, like 1 3/4
  • an exact decimal, like 0.75
  • a multiple of pi, like 12 pi or 2/3 pi

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