What is \(\sqrt{144}\)?
- A \(10\)
- B \(11\)
- C \(12\)
- D \(14\)
Check answer and explanation
Answer C: \(12\)
Because \(12\times12=144\), the square root of \(144\) is \(12\).
CH03-09 lesson
Introduction to Square Roots Learning Activity
A focused Grade 7 learning session for Introduction to Square Roots using visual models, worked examples, strategy guidance, and a short mastery check.
- 15
- minutes
- 6
- lesson parts
- 11
- practice items
Students will build Grade 7 mastery of introduction to square roots using models, equations, and test-style reasoning.
Student goal: I can solve problems involving introduction to square roots.
Helpful first:
Solving Real-World Problems with Rational Numbers
Learn the Idea
Introduction to Square Roots is part of Grade 7 The Number System. This activity focuses on the central idea students need before they move into independent practice.
Students will build Grade 7 mastery of introduction to square roots using models, equations, and test-style reasoning.
See the Math
| What to notice | How to use it |
|---|---|
| Numbers, units, labels, diagrams, or graphs | Identify what each part represents before calculating. |
| The relationship in the problem | Connect the model to an equation, comparison, or explanation. |
Use the figures and worked questions in the practice set below as the visual model for this skill.
Follow a Worked Example
Read the first practice question slowly. Decide what the question is asking, choose a strategy, solve, and then compare your reasoning with the answer explanation.
For Introduction to Square Roots, a strong worked example should show the setup, the calculation or model, and a final answer that matches the context.
Connect It to a Real Situation
Many Grade 7 test questions use real situations. Look for quantities, units, rates, measures, expressions, or data values that connect the math to the story.
After solving, explain what the answer means in the situation, not just the number you calculated.
Avoid Mistakes and Choose a Strategy
- Underline the exact question before solving.
- Label units, variables, or graph axes when they appear.
- Estimate first so unreasonable answers are easier to catch.
- Review missed questions and write the reason for each mistake.
Remember the Key Idea
I can solve problems involving introduction to square roots.
Use the warmup, guided question, practice set, and exit questions below to check whether this skill is ready or needs more practice.
Solve before opening the answer
Use scratch paper. The explanation matters more than simply seeing whether the choice is correct.
warmup
2 questionsWhich number is a perfect square?
- A \(15\)
- B \(25\)
- C \(35\)
- D \(45\)
Check answer and explanation
Answer B: \(25\)
Perfect squares are numbers like \(4\), \(9\), \(16\), \(25\) that are products of a whole number times itself. Since \(5 \times 5 = 25\), it is a perfect square.
guided
1 questionWhat is \(\sqrt{49}\)?
- A \(6\)
- B \(7\)
- C \(8\)
- D \(9\)
Check answer and explanation
Answer B: \(7\)
\(7 \times 7 = 49\), so \(\sqrt{49} = 7\).
practice
5 questionsA square garden has an area of \(100\) square meters. What is the length of one side of the garden?
- A \(8\) meters
- B \(9\) meters
- C \(10\) meters
- D \(11\) meters
Check answer and explanation
Answer C: \(10\) meters
The area of a square is \(s^2\). If the area is \(100\), then \(s^2 = 100\), so \(s = \sqrt{100} = 10\) meters.
What is \(\sqrt{64}\)?
- A \(6\)
- B \(8\)
- C \(9\)
- D \(7\)
Check answer and explanation
Answer B: \(8\)
\(8 \times 8 = 64\), therefore \(\sqrt{64} = 8\).
Which of the following is NOT a perfect square?
- A \(81\)
- B \(72\)
- C \(121\)
- D \(169\)
Check answer and explanation
Answer B: \(72\)
Perfect squares: \(81 = 9^2\), \(121 = 11^2\), \(169 = 13^2\). The number \(72\) is not a perfect square since no whole number times itself equals \(72\).
Between which two consecutive integers does \(\sqrt{50}\) lie?
- A between \(3\) and \(4\)
- B between \(5\) and \(6\)
- C between \(6\) and \(7\)
- D between \(7\) and \(8\)
Check answer and explanation
Answer D: between \(7\) and \(8\)
\(7^2 = 49\) and \(8^2 = 64\). Since \(49 < 50 < 64\), we know \(7 < \sqrt{50} < 8\).
What is \(\sqrt{169}\)?
- A \(12\)
- B \(13\)
- C \(14\)
- D \(15\)
Check answer and explanation
Answer B: \(13\)
\(13 \times 13 = 169\), so \(\sqrt{169} = 13\).
exit
3 questionsWhat is \(\sqrt{225}\)?
- A \(13\)
- B \(14\)
- C \(15\)
- D \(16\)
Check answer and explanation
Answer C: \(15\)
\(15 \times 15 = 225\), so \(\sqrt{225} = 15\).
A square tile has an area of \(169\) square inches. What is the side length of the tile?
- A \(11\) inches
- B \(12\) inches
- C \(13\) inches
- D \(14\) inches
Check answer and explanation
Answer C: \(13\) inches
Since area \(= s^2\) and \(169 = 13^2\), the side length is \(\sqrt{169} = 13\) inches.
What is \(\sqrt{1}\)?
- A \(0\)
- B \(1\)
- C \(2\)
- D undefined
Check answer and explanation
Answer B: \(1\)
\(1 \times 1 = 1\), so \(\sqrt{1} = 1\).
