Questions based on Square root Quiz

Explore the principles of square roots with these multiple-choice questions, including calculations with perfect and non-perfect squares, estimation, and properties of square roots. Strengthen your understanding of square root concepts essential for math proficiency.

1. Square Root of a Perfect Square

   What is the square root of 144?

   1. 24
   2. 14
   3. 16
   4. 12

   Explanation: The square root of 144 is 12 because 12 multiplied by itself equals 144. Option 14 is incorrect, as 14 squared is 196. Option 24, when squared, results in 576, and 16 squared is 256. Thus, 12 is the only correct answer among the choices.

2. Identifying Non-Perfect Square Roots

   Which value is closest to the square root of 50?

   1. 8
   2. 6
   3. 5.5
   4. 7.1

   Explanation: The square root of 49 is 7, and the square root of 64 is 8, so the square root of 50 should be just above 7. Option 7.1 is closest to √50, which is approximately 7.07. Option 6 and 5.5 are too low, and 8 is too high for this square root.

3. Properties of Square Roots

   If √x = 9, what is the value of x?

   1. 18
   2. 27
   3. 81
   4. 72

   Explanation: Since √x = 9, squaring both sides gives x = 81 because 9 × 9 = 81. Option 18 and 27 are much too small, and 72 is also not correct, as 8.5 squared is approximately 72.25. 81 is the only value that fits the condition given.

4. Simplifying Square Roots

   What is the simplified form of √72?

   1. 12
   2. 8
   3. 7√2
   4. 6√2

   Explanation: √72 can be rewritten as √(36 × 2), which simplifies to 6√2. Option 8 and 12 are whole numbers that do not simplify √72, and 7√2 is not a correct simplification since 7×7×2 is 98. Only 6√2 represents the proper simplification.

5. Operations with Square Roots

   Which of the following is equal to (√9) + (√16)?

   1. 8
   2. 7
   3. 10
   4. 9

   Explanation: The square root of 9 is 3 and the square root of 16 is 4. Adding them gives 3 + 4 = 7. Option 8 and 10 are incorrect sums, and 9 is the initial number under the radical, not the result of the operation. Therefore, 7 is the correct answer.