Rewrite each of the following radicals as a rational number or in simplest radical form. a. √3(√3-1)b. (5+√3)²c. (10+√11)(10-√11)

Answer:a.  Rational number 1.26Simplest radical 3 − √ 3b. Simplest radical 28 + 10 √ 3 Rational number 45.32c. Rational number 89Step-by-step explanation:a. √3(√3-1)To get the simplest radical Apply the distributive property. √3*√3-√3Combine using the product rule for radicals. √ 3*3+√3*−1Move  − 1  to the left of √3.√ 3*√ 3*3 - 1 *√3Multiply  3   by   3. √ 9 − 1 *√ 3 Rewrite  9  as  3 ^2 √3^2 -1 *√ 3 Pull terms out from under the radical, assuming positive real numbers. 3 − 1 *√ 3 Rewrite  − 1 √ 3  as  − √ 3 . 3 − √ 3Rational number 1.26b. (5+√3)²Expand (5+√3)²= 25 +5*√3+5*√3+3= 28 + 10 √ 3 Simplest radical 28 + 10 √ 3 Rational number 45.32c. (10+√11)(10-√11)Expand(10+√11)(10-√11)= 10*10+ 10*-√11+10*√11+√11*-√11=100+ 10*-√11+10*√11- 11=89- 10*√11+10*√11=89