Squares & Roots ✨
Unlock the power of geometry and numbers!
👤 Student Details
📖 Introduction
A Square of a number is the product obtained by multiplying the number by itself. For example, \(4 \times 4 = 16\). So, \(16\) is the square of \(4\), written as \(4^2 = 16\).
Visualizing \(4^2\):
It forms a perfect square shape with equal sides!
The Square Root (\(\sqrt{\text{ }}\)) is the inverse operation. \(\sqrt{16} = 4\) because \(4\) squared gives \(16\).
💡 Worked Examples
Example 1: Finding Square of \(15\)
Multiply \(15\) by itself: \(15 \times 15\)
Calculate: \(225\)
Example 2: Square Root by Factorization (\(\sqrt{64}\))
Prime Factors: \(2 \times 2 \times 2 \times 2 \times 2 \times 2\)
Make pairs: \((2 \times 2) \times (2 \times 2) \times (2 \times 2)\)
Take one from each pair: \(2 \times 2 \times 2 = 8\)
Example 3: Non-Perfect Squares
Is \(50\) a perfect square?
Prime Factors: \(2 \times 5 \times 5\).
Result: The number '\(2\)' does not have a pair. So, \(50\) is NOT a perfect square.
Example 4: Word Problem
A square garden has an area of \(144 \text{ m}^2\). Find its side length.
\(\text{Area} = \text{Side}^2\). So, \(\text{Side} = \sqrt{144}\).
Result: \(12 \text{ meters}\).
✏️ Practice Questions
1. Find the square of \(12\):
2. What is \(\sqrt{81}\)?
3. Find the square root of \(400\):
4. Side of a square with area \(49 \text{ cm}^2\)?
5. Square of \(0.5\)?
📝 Final Quiz
1. Which of the following is a perfect square?
2. The value of \(\sqrt{1.44}\) is:
3. How many zeros will be in the square of \(400\)?
4. Square of an odd number is always:
5. Find \(\sqrt{625}\)
6. A square field area is \(2500 \text{ m}^2\). Find its perimeter (\(P\)).
7. A Pythagorean triplet starts with \(6\). The other two numbers are:
8. The value of \((0.09)^2\) is:
9. Smallest number to multiply with \(20\) to make it a perfect square?
10. The unit digit of the square of \(77\) is: