Testinar Grade 7 math

Introduction to Square Roots

Students will build Grade 7 mastery of introduction to square roots using models, equations, and test-style reasoning.

CH03-09 The Number System

Directions Solve each problem. Show your reasoning on the page or on separate paper. Check the answer key only after finishing.

What is \(\sqrt{144}\)?
1. \(10\)
2. \(11\)
3. \(12\)
4. \(14\)
Which number is a perfect square?
1. \(15\)
2. \(25\)
3. \(35\)
4. \(45\)
What is \(\sqrt{49}\)?
1. \(6\)
2. \(7\)
3. \(8\)
4. \(9\)
A square garden has an area of \(100\) square meters. What is the length of one side of the garden?
1. \(8\) meters
2. \(9\) meters
3. \(10\) meters
4. \(11\) meters
What is \(\sqrt{64}\)?
1. \(6\)
2. \(8\)
3. \(9\)
4. \(7\)
Which of the following is NOT a perfect square?
1. \(81\)
2. \(72\)
3. \(121\)
4. \(169\)
Between which two consecutive integers does \(\sqrt{50}\) lie?
1. between \(3\) and \(4\)
2. between \(5\) and \(6\)
3. between \(6\) and \(7\)
4. between \(7\) and \(8\)
What is \(\sqrt{225}\)?
1. \(13\)
2. \(14\)
3. \(15\)
4. \(16\)

Teacher and parent reference

Answer key and explanations

C. \(12\)
Because \(12\times12=144\), the square root of \(144\) is \(12\).
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.
B. \(7\)
\(7 \times 7 = 49\), so \(\sqrt{49} = 7\).
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.
B. \(8\)
\(8 \times 8 = 64\), therefore \(\sqrt{64} = 8\).
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 \(72\).
D. between \(7\) and \(8\)
\(7^2 = 49\) and \(8^2 = 64\). Since \(49 < 50 < 64\), we know \(7 < \sqrt{50} < 8\).
C. \(15\)
\(15 \times 15 = 225\), so \(\sqrt{225} = 15\).