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Two Brackets

Part of the Radicals & Rational Exponents section of Coddy's Algebra 2 journey. Lesson 13 of 43.

Two brackets multiply the way they always have: every term in the first times every term in the second. Take (3 + √(2))(1 + √(2)). That gives four products: 3 times 1, 3 times √(2), √(2) times 1, and √(2) times √(2).

3 + 3√(2) + √(2) + 2

The last product is 2, because a root times itself is what is under it. Now collect: the numbers 3 and 2 make 5, and the roots make 4√(2). The answer is 5 + 4√(2).

Challenge

Expand and simplify (2 + √(3))(1 + √(3)).

Try it yourself

(2 + sqrt(3))(1 + sqrt(3))

Write it in simplest radical form

Test yourself

This lesson includes a short quiz. Start the lesson to answer it and track your progress.

All lessons in Radicals & Rational Exponents

1Simplifying Radicals

Roots and Powers Perfect Square Factors The Largest Square Letters Under the Root Cube Roots Recap: Simplifying Radicals

4Rationalizing

One Root Below A Number and a Root The Conjugate Below Recap: Rationalizing

7Powers and Roots Equations

Odd Powers Even Powers Fractional Powers Two Thirds Power Recap: Power Equations

2Adding & Subtracting Radicals

Like Radicals Simplify First Subtracting Recap: Adding Radicals

5Rational Exponents

One Over n m Over n Negative Exponents Exponent Rules Still Work Recap: Rational Exponents

8Radical Functions

Domain of a Root Evaluating Inverse of a Square Recap: Radical Functions

3Multiplying Radicals

Root Times Root Distributing a RootTwo BracketsConjugate Pairs Recap: Multiplying Radicals

6Radical Equations

Square Both Sides Isolate the Root First A False Answer Cube Root Equations Recap: Radical Equations

9Final Challenges

Final: Simplify and Add Final: Clear the Root Final: The Exponent Final: Check It Final: The Falling Ball