Part A: Subjective Questions

Note: Write the answers neatly on a sheet and submit them to your school subject teacher.

(1) Write the square root of 81.

Excellent! √81 = 9 because 9 × 9 = 81, making 81 a perfect square.

(2) Write the cube root of 64.

Perfect! ∛64 = 4 because 4 × 4 × 4 = 64, making 64 both a perfect square and perfect cube.

(3) Find the square root of 0.25.

Brilliant! √0.25 = 0.5 because 0.5 × 0.5 = 0.25, showing how square roots work with decimals.

(4) Which is the smallest 2-digit perfect square?

Outstanding! 16 = 4² is the smallest 2-digit perfect square (1-digit perfect squares are 1, 4, 9).

(5) Write the cube of 5.

Awesome! 5³ = 5 × 5 × 5 = 125, making 125 a perfect cube with cube root 5.

Drag each number to its correct category:

(1) Find the square root of 121 by the prime factorization method.

Step 1: Prime factorization of 121 = 11 × = 11²22

Step 2: √121 = √(11²) =

Excellent! Prime factorization method shows that √121 = 11 since 11 appears as a perfect pair.

(2) Find the cube root of 343.

Step 1: Check if 343 is a perfect

Step 2: × × = 343, so ∛343 =

Perfect! You correctly identified that 343 = 7³, so the cube root is 7.

(3) Write the smallest number which should be multiplied to 20 to make it a perfect square.

Step 1: Prime factorization of 20 = 2²2¹ × 5¹5²

Step 2: To make perfect square, multiply by

So the smallest number =

Brilliant! Since 20 = 2² × 5¹, we need another 5 to make 5² for a perfect square.

(4) The volume of a cube is 729 cm³. Find the length of its edge.

Step 1: Volume of cube = ³ = cm³

Step 2: Edge = ∛729 = cm

Outstanding! Since 9³ = 729, the edge length is 9 cm, demonstrating cube root application in geometry.

Test your understanding with these multiple choice questions:

1. The square root of 0.0001 is:

(a) 0.1 (b) 0.01 (c) 0.001 (d) 1

Correct! √0.0001 = 0.01 because 0.01 × 0.01 = 0.0001.

2. The cube root of 1000 is:

(a) 1 (b) 10 (c) 100 (d) 1000

Correct! ∛1000 = 10 because 10 × 10 × 10 = 1000.

3. The smallest 3-digit perfect square is:

(a) 100 (b) 121 (c) 144 (d) 169

Correct! 100 = 10² is the smallest 3-digit perfect square.

4. The length of the side of a cube whose volume is 27 cm³ is:

(a) 9 cm (b) 3 cm (c) 6 cm (d) 12 cm

Correct! If volume = 27 cm³, then side = ∛27 = 3 cm.

5. Which of the following is NOT a perfect cube?

(a) 27 (b) 64 (c) 100 (d) 125

Correct! 100 is not a perfect cube. (27 = 3³, 64 = 4³, 125 = 5³).

🎉 Outstanding! You've Mastered Square Roots and Cube Roots! Here's what you accomplished:

✓ Perfect Squares Recognition: Identifying numbers like 16, 25, 36, 49, 64, 81, 100, 121, 144

✓ Perfect Cubes Recognition: Identifying numbers like 8, 27, 64, 125, 216, 343, 729, 1000

✓ Square Root Calculations: Finding square roots using prime factorization and estimation

✓ Cube Root Calculations: Finding cube roots of perfect cubes

✓ Decimal Roots: Working with square roots of decimal numbers

✓ Prime Factorization Method: Using systematic factorization to find roots

✓ Real-World Applications: Solving problems involving cube volumes and square areas

✓ Perfect Square/Cube Creation: Finding factors needed to make numbers perfect squares or cubes

Your strong foundation in square and cube roots prepares you for advanced topics like irrational numbers, algebraic expressions, and geometric applications!