Math Problem Statement

Express in simplest radical form. minus, 7, square root of, 3, end square root, minus, square root of, 3, end square root −7 3 ​ − 3 ​

Solution

We are tasked with simplifying the following expression:

733.-7\sqrt{3} - \sqrt{3}.

Step 1: Combine like terms

Since both terms have the common factor 3\sqrt{3}, we can factor it out:

733=(71)3.-7\sqrt{3} - \sqrt{3} = (-7 - 1)\sqrt{3}.

Step 2: Simplify the coefficient

Simplify the expression inside the parentheses:

71=8.-7 - 1 = -8.

Thus, the expression becomes:

83.-8\sqrt{3}.

Final Answer:

83\boxed{-8\sqrt{3}}

Would you like a detailed explanation of the factoring process or have any related questions?


Related Questions:

  1. What are like terms in a radical expression?
  2. How do you simplify expressions with square roots?
  3. Can you explain the distributive property when working with radicals?
  4. How would you simplify 52+325\sqrt{2} + 3\sqrt{2}?
  5. What is the significance of writing radicals in their simplest form?

Tip:

When simplifying radical expressions, always look for common factors or terms to combine them easily.

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Math Problem Analysis

Mathematical Concepts

Radical Expressions
Simplification
Like Terms

Formulas

n√a + m√a = (n + m)√a
Factoring

Theorems

Distributive Property
Simplification of Radicals

Suitable Grade Level

Grades 8-10