Math Problem Statement

√5 + 6√20

Solution

The image contains a mathematical expression to be simplified. The expression is:

5+620\sqrt{5} + 6\sqrt{20}

To simplify this, let's work through it step-by-step:

  1. Simplify the square root of 20: 20=4×5=4×5=25\sqrt{20} = \sqrt{4 \times 5} = \sqrt{4} \times \sqrt{5} = 2\sqrt{5}

  2. Substitute this into the original expression: 5+620=5+6(25)=5+125\sqrt{5} + 6\sqrt{20} = \sqrt{5} + 6(2\sqrt{5}) = \sqrt{5} + 12\sqrt{5}

  3. Combine like terms: 5+125=135\sqrt{5} + 12\sqrt{5} = 13\sqrt{5}

So, the simplified result is: 13513\sqrt{5}

Would you like further details or have any questions? Here are five related questions to expand on this topic:

  1. How do you simplify square roots involving products of numbers?
  2. Can you always combine terms with square roots in an expression?
  3. What is the process for rationalizing a denominator that contains a square root?
  4. How would you handle expressions with cube roots, such as 203\sqrt[3]{20}?
  5. How does factoring play a role in simplifying square roots?

Tip: Always look for perfect square factors when simplifying square roots to make the process easier.

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Math Problem Analysis

Mathematical Concepts

Simplification of square roots
Radicals
Combining like terms

Formulas

√a * √b = √(a * b)
Simplify square roots by factoring

Theorems

Properties of square roots

Suitable Grade Level

Grades 8-10