Squares and Square Roots Practice Problems

• Q1. What is the square of 17?

  • a) 269

  • b) 289

  • c) 297

  • d) 272

• Q2. The square of 25 is:

  • a) 50

  • b) 125

  • c) 625

  • d) 225

• Q3. Using patterns, the square of 45 is:

  • a) 2025

  • b) 1825

  • c) 1625

  • d) 1525

• Q4. What is the square root of 144?

  • a) 10

  • b) 11

  • c) 12

  • d) 13

• Q5. The square root of 529 is:

  • a) 21

  • b) 22

  • c) 23

  • d) 24

• Q6. Find $\sqrt{256}$:

  • a) 14

  • b) 15

  • c) 16

  • d) 18

• Q7. What is the square root of 1024?

  • a) 16

  • b) 24

  • c) 32

  • d) 64

• Q8. The square root of 1.69 is:

  • a) 1.1

  • b) 1.2

  • c) 1.3

  • d) 1.4

• Q9. Simplify $\sqrt{50}$:

  • a) $10\sqrt{5}$

  • b) $5\sqrt{2}$

  • c) $25\sqrt{2}$

  • d) $2\sqrt{25}$

• Q10. Which of the following statements is false?

  • a) $\sqrt{9 + 16} = \sqrt{9} + \sqrt{16}$

  • b) $\sqrt{25} = 5$

  • c) $\sqrt{8 \times 18} = 12$

  • d) $\sqrt{0.01} = 0.1$

Squares and Square Roots: Problems & Explanations

Q1.What is the square of 17?

• Answer: b) 289

• Explanation: To find the square of a number, you multiply it by itself ($17 \times 17$). Calculating $17 \times 10 = 170$ and $17 \times 7 = 119$, then $170 + 119 = 289$.

Q2.The square of 25 is:

• Answer: c) 625

• Explanation: Squaring 25 means calculating $25 \times 25$. A quick mental trick for numbers ending in 5 is to multiply the first digit (2) by the next consecutive integer (3), which gives 6, and then append 25 at the end.

Q3.Using patterns, the square of 45 is:

• Answer: a) 2025

• Explanation: Using the pattern for squares of numbers ending in 5:

  1. Take the tens digit (4) and multiply it by the next number (5): $4 \times 5 = 20$.

  2. Write “25” after it.

  3. Result: 2025.

Q4.What is the square root of 144?

• Answer: c) 12

• Explanation: You are looking for a number that, when multiplied by itself, equals 144. Since $12 \times 12 = 144$, the square root is 12.

Q5.The square root of 529 is:

• Answer: c) 23

• Explanation: You can use estimation or prime factorization. Since $20^2 = 400$ and $30^2 = 900$, the answer must be between 20 and 30. Because the last digit is 9, the root must end in 3 or 7. Testing 23: $23 \times 23 = 529$.

Q6.Find $\sqrt{256}$.

• Answer: c) 16

• Explanation: Through repeated subtraction or prime factorization ($2^8$), we find that $16 \times 16 = 256$.

Q7.What is the square root of 1024?

• Answer: c) 32

• Explanation: $30^2 = 900$ and $40^2 = 1600$. The number ends in 4, so the square root must end in 2 or 8. Testing 32: $32 \times 32 = 1024$.

Q8.The square root of 1.69 is:

• Answer: c) 1.3

• Explanation: Think of this as $\sqrt{\frac{169}{100}}$. The square root of 169 is 13, and the square root of 100 is 10. $\frac{13}{10} = 1.3$.

Q9.Simplify $\sqrt{50}$.

• Answer: b) $5\sqrt{2}$

• Explanation: Break 50 down into its factors, looking for a perfect square: $\sqrt{25 \times 2}$. Since the square root of 25 is 5, it comes out of the radical, leaving $\sqrt{2}$ inside.

Q10.Which of the following statements is false?

• Answer: a) $\sqrt{9 + 16} = \sqrt{9} + \sqrt{16}$

• Explanation: This is false because of the order of operations.

  • Left side: $\sqrt{9 + 16} = \sqrt{25} = 5$.

  • Right side: $\sqrt{9} + \sqrt{16} = 3 + 4 = 7$.

  • Since $5 \neq 7$, the statement is incorrect.