Square and Square Roots Lesson-  Definition, Tables, Examples

Lesson Overview

• Square and Square Roots Table
• What Are Perfect Squares?
• How to Find the Square
• Properties of Square Numbers
• Solved Examples on Squares and Square Roots
• Square and Square Roots Assessments

What Are Squares and Square Roots?

A square is the result of multiplying a number by itself. 

For example, 4 × 4 = 16, so 16 is the square of 4. 

A square root is the number you multiply by itself to get the square. 

For example, the square root of 16 is 4 because 4 × 4 = 16.

Square and Square Roots Table

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Square and square roots-TEST 1

What Are Perfect Squares?

Perfect squares are numbers obtained by squaring whole numbers. Examples are:

• 1 is a perfect square because 1 × 1 = 1.
• 25 is a perfect square because 5 × 5 = 25.
• 64 is a perfect square because 8 × 8 = 64.

How to Find the Square

Finding the square of a number is simple. Follow these steps:

1. Understand what a square means
   • The square of a number is the result of multiplying that number by itself.
   • For example, if the number is 3, its square is 3 × 3 = 9.
2. Write the number twice
   • Take the number and write it down two times as a multiplication.
   • Example: To find the square of 5, write 5 × 5.
3. Multiply the number by itself
   • Perform the multiplication.
   • Example: 5 × 5 = 25. So, the square of 5 is 25.
4. Use a calculator if needed
   • If the number is large, use a calculator to make the multiplication faster and more accurate.

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How to simplify square roots quiz

Properties of Square Numbers

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Squares And Square Roots Quiz Questions And Answers

Solved Examples on Squares and Square Roots

Example 1: Find the square of 7.
Solution:

• The square of a number is obtained by multiplying the number by itself.
• Square of 7 = 7 × 7 = 49.
• Answer: 49

Example 2: Find the square root of 81.
Solution:

• The square root is the number which, when multiplied by itself, gives the square.
• We know 9 × 9 = 81.
• Therefore, the square root of 81 is 9.
• Answer: 9

Example 3: Check if 36 is a perfect square.
Solution:

• A number is a perfect square if it can be expressed as the square of a whole number.
• Find the square root of 36.
  • 6 × 6 = 36, so the square root of 36 is 6.
• Since the square root is a whole number, 36 is a perfect square.
• Answer: Yes, 36 is a perfect square.

Example 4: Calculate the square of 15 and explain if it is even or odd.
Solution:

• Square of 15 = 15 × 15 = 225.
• 15 is an odd number, and the square of an odd number is always odd.
• Answer: 225 (odd number).

Example 5: Find the square root of 144 and verify the result.
Solution:

• The square root of 144 is the number that, when multiplied by itself, equals 144.
• 12 × 12 = 144, so the square root of 144 is 12.
• Verification: 12 × 12 = 144 (Correct).
• Answer: 12

Square and Square Roots Assessments

1. Write the squares of numbers 1 to 15.
2. Find the square roots of 1, 16, 81, and 100.
3. Check whether 49 and 72 are perfect squares by finding their square roots.