This document provides instructions for working with radicals and irrational square roots, including: 1) How to simplify irrational square roots by looking for perfect squares within numbers. 2) How to add radicals by expressing them with the same radicand and using the distributive property. 3) How to subtract radicals by expressing them with the same radicand and using the distributive property. The document uses examples such as √50 = 5√2 and 4√7 + 5√7 = 9√7 to demonstrate techniques for simplifying radicals.

1. Radicals are Radical!

2. Do Now √ 169 5. 5√28-2√45 14√75 6. 3 √45+7√36 3√160 5√3 + 2√75

3. Rational Square Roots Square Root- If a ²= b, then a is the square root of b. Example - 5² = 25, √25 = 5. 5 is the square root of 25. Example - 9² = 81. √81 = 9. 9 is the square root of 81.

4. Simplifying Irrational Square Roots Irrational square roots are numbers that cannot be expressed as fractions. While solving irrational square roots, look for perfect square within the number. (4,9,16…) Example: √50 = √25x2 = 5√2 Example: √24 = √6x4 = 2√6

5. Adding Radicals To simplify the sums of square-root radicals 1.) Express each radical in simplest form. 2.) Use the Distributive property to add the radicals with like radicands. Example.) 4 √7 + 5√7 = (4+5)√7 = 9√7 Example.) √24 +√6 = √6x4 + √6 = 2√6 + √6 = 3√6

6. Subtracting Radicals To simplify the differences of square-root radicals: 1.) Express each radical in simplest form. 2.) Use the distributive property to subtract radicals with like radicands. Example.) 8√3 - 5√3 = (8-5)√3 = 3√3 Example.)√27 - √3 = √9x3 - √3 = 3√3 - √3= 2√3

7. Assessment If you are up for the challenge, click here for our quiz