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Two Brackets

Part of the Radicals & Rational Exponents section of Coddy's Algebra 2 journey. Lesson 10 of 40.

Two brackets multiply the way they always have: every term in the first times every term in the second. Take $\left(3+\sqrt{2}\right)\left(1+\sqrt{2}\right)$ . That gives four products: 3 times 1, 3 times $\sqrt{2}$ , $\sqrt{2}$ times 1, and $\sqrt{2}$ times $\sqrt{2}$ .

$3+3\sqrt{2}+\sqrt{2}+2$

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 $4\sqrt{2}$ . The answer is $5+4\sqrt{2}$ .

Challenge

Expand and simplify $\left(2+\sqrt{3}\right)\left(1+\sqrt{3}\right)$ .

Try it yourself

\left(2+\sqrt{3}\right)\left(1+\sqrt{3}\right)

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

1Simplest Form

Perfect Square Factors Like Radicals Simplify First Recap: Adding 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

2Letters and Cube Roots

Letters Under the Root Cube Roots Recap: Simplifying 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