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## Algebraic Roots and Radicals

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**Algebraic Roots and Radicals**Simplifying Perfect Square Radical Expressions Approximating Square Roots Click on topic to go to that section. Rational & Irrational Numbers Radical Expressions Containing Variables Simplifying Non-Perfect Square Radicands Simplifying Roots of Variables Operations with Radicals Pythagorean Theorem Distance Formula Intro to Trig Solving Right Triangles**Simplifying Perfect Square**Radical Expressions Return to Table of Contents**Can you recall the perfect squares from 1 to 169?**12 = 82 = 22 = 92 = 32 = 102 = 42 = 112 = 52 = 122 = 62 = 132 = 202 = 72 =**Square Root Of A Number**Recall: If b2 = a, then b is a square root of a. Example: If 42 = 16, then 4 is a square root of 16 What is a square root of 25? 64? 100?**Square Root Of A Number**Square roots are written with a radical symbol Positive square root: = 4 Negative square root: - = - 4 Positive & negative square roots: = 4 Negative numbers have no real square roots no real roots because there is no real number that, when squared, would equal -16.**Is there a difference between**& ? Which expression has no real roots? Evaluate the expression**Evaluate the expression**is not real**2**?**3**= ?**6**= ? A 3 B -3 C No real roots**7**The expression equal to is equivalent to a positive integer when b is A -10 B 64 C 16 D 4**Square Roots of Fractions**a b = b0 4 16 49 = = 7**8**C A B D no real solution**9**C A B D no real solution**10**C A B D no real solution**11**C A B D no real solution**12**C A B D no real solution**Square Roots of Decimals**Recall:**To find the square root of a decimal, convert the decimal**to a fraction first. Follow your steps for square roots of fractions. = .2 = .05 = .3**13**Evaluate B A C D No Real Solution**14**Evaluate B .6 A .06 C 6 D No Real Solution**15**Evaluate B 11 A .11 C 1.1 D No Real Solution**16**Evaluate B .08 A .8 C D No Real Solution**17**Evaluate B A C D No Real Solution**Approximating**Square Roots Return to Table of Contents**Approximating a Square Root**Approximate to the nearest integer < Identify perfect squares closest to 38 Take square root < < 6 7 < Answer: Because 38 is closer to 36 than to 49, is closer to 6 than to 7. So, to the nearest integer, = 6**Approximate to the nearest integer**< < Identify perfect squares closest to 70 Take square root Identify nearest integer < <**18**Approximate to the nearest integer**19**Approximate to the nearest integer**20**Approximate to the nearest integer**21**Approximate to the nearest integer**22**Approximate to the nearest integer**23**The expression is a number between A 3 and 9 B 8 and 9 C 9 and 10 D 46 and 47**Rational & Irrational**Numbers Return to Table of Contents**Rational & Irrational Numbers**is rational because the radicand (number under the radical) is a perfect square If a radicand is not a perfect square, the root is said to be irrational. Ex:**24**Rational or Irrational? A Rational B Irrational**25**Rational or Irrational? A Rational B Irrational**26**Rational or Irrational? A Rational B Irrational**27**Rational or Irrational? A Rational B Irrational**28**Rational or Irrational? A Rational B Irrational**29**Which is a rational number? A B p C D**30**Given the statement: “If x is a rational number, then is irrational.”Which value of x makes the statement false? A B 2 C 3 D 4**Radical Expressions**Containing Variables Return to Table of Contents**Square Roots of Variables**To take the square root of a variable rewrite its exponent as the square of a power. = =**Square Roots of Variables**If the square root of a variable raised to an even power has a variable raised to an odd power for ananswer, the answer must have absolutevalue signs. This ensures that the answer will be positive. By Definition...