Math Problem Statement

√56

Solution

The square root of 56 is approximately:

567.483\sqrt{56} \approx 7.483

Since 56 is not a perfect square, the square root is an irrational number, meaning it cannot be expressed as a simple fraction. It can also be simplified as follows:

56=4×14=4×14=214\sqrt{56} = \sqrt{4 \times 14} = \sqrt{4} \times \sqrt{14} = 2\sqrt{14}

Thus, the simplified form is 2142\sqrt{14}, and the decimal approximation is about 7.483.

Would you like more details or have any questions?

Here are five related questions to explore further:

  1. What is the square root of 14 in simplified form?
  2. How do you calculate the square root of non-perfect squares?
  3. What are perfect squares, and how do they relate to simplifying square roots?
  4. Can you simplify 98\sqrt{98} in a similar way?
  5. How do you approximate square roots without a calculator?

Tip: When simplifying square roots, look for perfect square factors inside the radical sign to simplify the expression.

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Math Problem Analysis

Mathematical Concepts

Square Roots
Simplification of Radicals
Irrational Numbers

Formulas

√(a × b) = √a × √b

Theorems

Properties of Square Roots

Suitable Grade Level

Grades 7-10