Math Problem Statement

$$$$ \sqrt3\left(\sqrt{5-\sqrt6}\right)

Solution

It looks like you've input part of an expression:

3(56)\sqrt{3} \left( \sqrt{5 - \sqrt{6}} \right)

Is this the expression you want help simplifying, or are you looking for something else? Let me know if you'd like assistance solving this or working through its steps!

Would you like to explore the steps involved in simplifying it? Here's how we can approach:

  1. First, break down the inner square root: 56\sqrt{5 - \sqrt{6}}.
  2. Look for potential rational approximations or simplifications within the nested radical.
  3. Multiply the result by 3\sqrt{3} once the inner radical is simplified.

Feel free to ask for further details or clarification!

Related questions:

  1. How do you simplify nested radicals?
  2. What is the general rule for multiplying square roots?
  3. Are there standard techniques to simplify expressions like ab\sqrt{a - \sqrt{b}}?
  4. How can approximations help simplify square root expressions?
  5. How can we approach more complex nested radicals?

Tip: When working with nested square roots, always check for simplifications inside the radicals first.

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Math Problem Analysis

Mathematical Concepts

Radicals
Nested Radicals
Simplification

Formulas

\sqrt{a} \times \sqrt{b} = \sqrt{a \times b}
Simplifying nested square roots: \sqrt{a - \sqrt{b}}

Theorems

Properties of Square Roots
Radical Simplification Theorem

Suitable Grade Level

Grades 10-12