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Quizzes > High School Quizzes > Mathematics

Square Root Practice Quiz

Sharpen your skills with engaging problems

Difficulty: Moderate
Grade: Grade 7
Study OutcomesCheat Sheet
Colorful paper art promoting Square Root Showdown, a dynamic math quiz for middle school students.

What is the square root of 16?
5
3
2
4
Since 4 multiplied by 4 equals 16, the square root of 16 is 4. This basic computation is essential for understanding square root concepts.
Which of these numbers is a perfect square?
25
30
20
18
A perfect square is a number that can be written as the square of an integer. Since 25 equals 5 squared, it is the perfect square among the options.
Simplify the expression √9.
2
4
5
3
The number 3 multiplied by itself gives 9, so √9 is 3. This problem reinforces the relationship between squares and square roots.
What is the square root of 49?
7
6
5
8
Since 7 times 7 equals 49, the square root of 49 is 7. Recognizing perfect squares like this is key to mastering square root concepts.
What is the square root of 81?
7
9
8
10
The number 9 multiplied by 9 gives 81, which makes 9 the square root of 81. This straightforward problem reinforces the concept of perfect squares.
What is the simplified form of √50?
25√2
5√2
2√5
√2
The number 50 can be factored as 25 × 2, so √50 = √25 × √2 = 5√2. This exercise illustrates how to simplify square roots by factoring out perfect squares.
If √x = 8, what is the value of x?
8
32
64
16
Squaring both sides of the equation √x = 8 gives x = 8², which is 64. This problem emphasizes the inverse relationship between squaring and square roots.
Which expression is equivalent to √18?
√6
√20
3√2
2√3
Breaking 18 into 9 × 2 allows you to simplify √18 to √9 × √2, which equals 3√2. Recognizing factor pairs helps when simplifying radicals.
Solve for x: √x + 2 = 10.
100
64
16
8
Subtract 2 from both sides to get √x = 8, then square both sides to find x = 64. This step-by-step approach is crucial when solving equations with square roots.
What is the value of (√36)²?
6
18
72
36
The square root of 36 is 6 and squaring 6 gives back 36, demonstrating that (√a)² returns the original number a. This reinforces the inverse operations of square roots and squaring.
Simplify: √(4x²) where x is a positive number.
4x
2x
x²
2
Since √4 is 2 and √(x²) is x (given x is positive), the expression simplifies to 2x. This problem demonstrates the property of square roots applied to products.
Which of the following is NOT equivalent to √27?
9√3
√(9×3)
√27
3√3
Simplifying √27 gives 3√3, so the expressions √(9×3) and √27 are equivalent. The expression 9√3 is much larger and does not equal √27.
Express the square root of 0.25 as a decimal.
0.5
1.0
2.0
0.25
Since 0.5 multiplied by 0.5 equals 0.25, the square root of 0.25 is 0.5. This conversion helps bridge the understanding between radicals and decimals.
Which property of square roots is correctly represented by the equation √(a × b) = ?
√a + √b
√a - √b
√a × √b
a × b
The square root of a product is equal to the product of the square roots of the factors, provided both a and b are nonnegative. This is a fundamental property of radicals that is used frequently in algebra.
If 3√x = 12, what is the value of x?
12
16
4
8
Dividing both sides by 3 gives √x = 4, and squaring 4 results in x = 16. This problem reinforces solving linear equations involving square roots.
Solve for x: √(2x + 3) = 5.
12
10
9
11
Squaring both sides of the equation yields 2x + 3 = 25. Subtracting 3 and then dividing by 2 gives x = 11, demonstrating a systematic approach to solving radical equations.
Find the solution of the equation: √(x + 5) = x - 1.
-1
3
4
1
After squaring both sides of the equation, a quadratic is obtained, and potential solutions must be checked against the domain restriction. Only x = 4 satisfies the original equation when verified.
Simplify the expression: √50 + √18 - √8.
6√2
2√2
8√2
√60
Simplify each radical separately: √50 becomes 5√2, √18 becomes 3√2, and √8 becomes 2√2. Combining like terms (5√2 + 3√2 - 2√2) gives 6√2.
Find the positive value of x that satisfies: x/2 = √x.
8
4
2
0
By rewriting the equation as x = 2√x and then dividing by √x (assuming x > 0), we get √x = 2, which leads to x = 4. This problem demonstrates solving for variables in radical equations.
Which equation correctly represents the area A of a square with side length √x?
A = x²
A = x
A = 2x
A = √x
The area of a square is found by squaring its side length. Since the side length here is √x, squaring it results in x, which is the correct representation of the area.
0
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Study Outcomes

  1. Understand the definition and properties of square roots.
  2. Apply square root operations to simplify expressions.
  3. Analyze problems to identify when to use square roots in calculations.
  4. Solve equations involving square roots accurately.
  5. Evaluate and interpret the practical applications of square roots in problem-solving.

Square Root Quiz - Practice Test Cheat Sheet

  1. Definition of Square Roots - A square root of a number is the value that, when multiplied by itself, returns the original number; it's like "unsquaring" a perfect square. Think of √9 = 3 - when you square 3, you get back to 9! BYJU'S: Square Root Basics
  2. Key Properties - Square roots follow handy rules: √a × √b = √(a × b) and √(a/b) = √a / √b, making complex expressions simpler in a snap. Master these and you'll slice through algebra problems like a pro! GeeksforGeeks: Square Root Formulas
  3. Perfect vs. Non‑Perfect Squares - Perfect squares (like 16) have whole-number roots (√16 = 4), while non-perfect squares (like 17) give you irrational results - numbers that never end or repeat. Spotting them helps predict when you'll need a calculator! Mathstoon: Perfect Square Rules
  4. Simplifying Radicals - Break the radicand into prime factors, pair them up, and pull them outside the root. For instance, √72 = √(36 × 2) = 6√2 - easy peasy prime squeezy! OpenStax: Radical Simplification
  5. Imaginary Square Roots - The square root of a negative number isn't real - it's imaginary. For example, √(−9) = 3i, where i represents √(−1). Embrace the imaginary world to solve tougher equations! Mathstoon: Imaginary Numbers
  6. Exponent Notation - You can write √a as a^(1/2), turning root operations into exponents. This trick is a lifesaver for advanced algebra and calculus manipulations! OnlineMath4All: Roots as Exponents
  7. Non‑Square Endings - Numbers ending in 2, 3, 7, or 8 can never be perfect squares, so their roots are always irrational - no neat decimal will ever appear! Keep an eye on those last digits. OnlineMath4All: Irrational Roots
  8. Even‑Odd Root Patterns - If your perfect square is even, its root is even (√144 = 12); if it's odd, the root is odd (√225 = 15). These patterns let you predict roots in a flash. OnlineMath4All: Parity in Roots
  9. Inverse Relation - Remember: squaring and square rooting are inverse operations. So if x² = y, then √y = x - a concept that ties together many algebraic solutions. BYJU'S: Inverse Functions
  10. Real‑Life Applications - Square roots aren't just for theory; use them in geometry to find distances with the Pythagorean theorem (c = √(a² + b²)), in physics for wave functions, and even in finance for volatility models. GeeksforGeeks: Practical Uses
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