Math Problem Statement

<-140\sqrt{140}<

Solution

The expression you provided is 140\sqrt{140}, which represents the square root of 140. Let's simplify it as much as possible.

  1. First, we can factor 140 into its prime factors: 140=22×5×7140 = 2^2 \times 5 \times 7

  2. Now, apply the square root: 140=22×5×7=235\sqrt{140} = \sqrt{2^2 \times 5 \times 7} = 2\sqrt{35}

Thus, the simplified form of 140\sqrt{140} is 2352\sqrt{35}.

Approximate Decimal Value:

If you need an approximate decimal value for 140\sqrt{140}, it is: 14011.83\sqrt{140} \approx 11.83

Would you like more details or have any questions about this process?


Here are some related questions for practice:

  1. What is the simplified form of 180\sqrt{180}?
  2. How do you simplify 50\sqrt{50}?
  3. What is the decimal approximation of 75\sqrt{75}?
  4. How do you express 48\sqrt{48} in simplest radical form?
  5. What are the prime factors of 140?

Tip: Always try to find the largest perfect square factor when simplifying square roots!

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Math Problem Analysis

Mathematical Concepts

Simplification
Radicals
Prime Factorization

Formulas

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

Theorems

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Suitable Grade Level

Grades 8-10