Math Problem Statement

simplify 40\sqrt{40}

Solution

To simplify 40\sqrt{40}, follow these steps:

  1. Factor 40 into its prime factors: 40=23×540 = 2^3 \times 5

  2. Group the factors to simplify the square root. We can rewrite 40\sqrt{40} as: 40=4×10=4×10\sqrt{40} = \sqrt{4 \times 10} = \sqrt{4} \times \sqrt{10}

  3. Simplify 4\sqrt{4}, which is 2: 40=210\sqrt{40} = 2\sqrt{10}

So, the simplified form of 40\sqrt{40} is: 210\boxed{2\sqrt{10}}

Would you like to explore more on this topic or need further clarification?

Here are 5 questions to deepen your understanding:

  1. How do you simplify other square roots like 72\sqrt{72}?
  2. What is the square root of 50 in its simplest form?
  3. How can you express a2×b\sqrt{a^2 \times b} in simplified form?
  4. How does simplifying square roots relate to factoring numbers?
  5. What is the difference between simplifying square roots and calculating their decimal approximations?

Tip: When simplifying square roots, always look for perfect square factors to make the process easier.

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Math Problem Analysis

Mathematical Concepts

Square Roots
Prime Factorization
Simplification of Radicals

Formulas

\( \sqrt{a \times b} = \sqrt{a} \times \sqrt{b} \)

Theorems

Product Property of Square Roots

Suitable Grade Level

Grades 6-8