Math Problem Statement

Simplify:sqrt(80)

Solution

The expression 80\sqrt{80} can be simplified by breaking down 80 into its prime factors.

  1. Start by finding the prime factorization of 80: 80=2×40=2×2×20=2×2×2×10=2×2×2×2×5=24×580 = 2 \times 40 = 2 \times 2 \times 20 = 2 \times 2 \times 2 \times 10 = 2 \times 2 \times 2 \times 2 \times 5 = 2^4 \times 5

  2. Then, apply the square root to the prime factorization: 80=24×5\sqrt{80} = \sqrt{2^4 \times 5}

  3. Since 24=22=4\sqrt{2^4} = 2^2 = 4, you can simplify the square root: 80=45\sqrt{80} = 4\sqrt{5}

So, the simplified form of 80\sqrt{80} is 454\sqrt{5}.

Would you like any further details or have any questions?

Here are some related questions you might find useful:

  1. How would you simplify 200\sqrt{200}?
  2. What is the square root of 7272 simplified?
  3. How do you express 45\sqrt{45} in its simplest form?
  4. Can you simplify 50\sqrt{50}?
  5. What is the square root of 1818 simplified?

Tip: When simplifying square roots, look for perfect square factors.

Ask a new question for Free

By Image

Drop file here or Click Here to upload

Math Problem Analysis

Mathematical Concepts

Square Roots
Prime Factorization

Formulas

-

Theorems

-

Suitable Grade Level

Grades 9-12