Math Problem Statement

Match the cube roots and square roots with their values: √4, ∛27, √64, √49, and ∛1,000.

Solution

Let's solve this matching puzzle step by step by finding the square roots and cube roots of the given numbers:

  1. √4: This is the square root of 4. The square root of 4 is 2.
  2. √27: This is the cube root of 27. The cube root of 27 is 3 because 3³ = 27.
  3. √64: This is the square root of 64. The square root of 64 is 8.
  4. √49: This is the square root of 49. The square root of 49 is 7.
  5. √1,000: This is the cube root of 1,000. The cube root of 1,000 is 10 because 10³ = 1,000.

Matches:

  • √4 → 2
  • √27 → 3
  • √64 → 8
  • √49 → 7
  • √1,000 → 10

Let me know if you'd like any more clarifications or help with similar problems!


Here are some related questions you might find interesting:

  1. What is the square root of 81?
  2. How do you find cube roots for numbers like 512 or 1000?
  3. Can you explain the difference between square roots and cube roots in simple terms?
  4. What are the properties of cube roots for perfect cubes?
  5. How do you simplify square roots or cube roots of large numbers?

Tip: To find the square root of a number, you can use a calculator or look for a perfect square (like 1, 4, 9, 16, etc.). Cube roots work similarly with perfect cubes (like 1, 8, 27, 64).

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Math Problem Analysis

Mathematical Concepts

Square Roots
Cube Roots
Radicals
Perfect Squares
Perfect Cubes

Formulas

√x (square root) where √x * √x = x
∛x (cube root) where ∛x * ∛x * ∛x = x

Theorems

Radical Simplification Rules

Suitable Grade Level

Grades 5-7