Math Problem Statement

Simplify the expression (√45 - √5)^2

Solution

The expression shown in the image is:

(455)2\left( \sqrt{45} - \sqrt{5} \right)^2

Steps to Simplify:

  1. Simplify the square roots:

    • 45=9×5=35\sqrt{45} = \sqrt{9 \times 5} = 3\sqrt{5}
    • 5\sqrt{5} remains as is.

    So, the expression becomes: (355)2\left( 3\sqrt{5} - \sqrt{5} \right)^2

  2. Factor out the common term 5\sqrt{5}: (355)=5(31)=25\left( 3\sqrt{5} - \sqrt{5} \right) = \sqrt{5}(3 - 1) = 2\sqrt{5}

    Now the expression is: \

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Math Problem Analysis

Mathematical Concepts

Algebra
Square Roots
Factoring

Formulas

√(a * b) = √a * √b
(a - b)^2 = a^2 - 2ab + b^2

Theorems

Distributive Property

Suitable Grade Level

Grades 9-11