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## Simplifying square roots

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**Simplifying**square roots**Do these expressions have another exact representation of**the value? Yes, the square root of 4 is also 2 because 2 times 2 equals 4. Yes, the square root of 8 is also 2 times the square root of 2 or 2 square roots of 2 which is also written as 2 . No, the square root of 13 can not be renamed or simplified.**Standard: M8N1. Students will understand different**representations of numbers including square roots, exponents, and scientific notation.g. Simplify, add, subtract, multiply, and divide expressions containing square roots. Essential Question: How do I simplify a square root?**If 92 = 81 then 9 is a square rootof 81 or = 9.**In the expression , is the radical signand64 is the radicand.**Find the principle square root of 64. This is also written**as . = 8 • Find the negative square root of 0.04. This is also written as : . [reminder: .04 is 4 hundredths; the square root of 4 is 2; the square root of one hundredth is one tenth] = - 0.2**3. Find the square roots:**11, -11 This can also be written ±11. 4. Find the square root: 21 5. Find the square root:**What numbers are squares?**1 x 1 = 1 2 x 2 = 4 3 x 3 = 9 4 x 4 = 16 5 x 5 = 25 6 x 6 = 36 49, 64, 81, 100, 121, 144, ...**1. Simplify**Factor 80. 80 = 2 x 2 x 2 x 2 x 5 Now, you may “take out” pairs of like factors = You did it! =**2. Simplify**Factoring 180 into prime factors you get 2 x 2 x 3 x 3 x 5. Yes! Good job!**Now, try one by yourself. Simplify and see if your**answer is below. Did you get it? Congratulations!!! 1. . 2. . 3. . 4..**3. Simplify**Simplify the numerator and denominator.**4. Simplify**Simplify the numerator and denominator. You could also solve this problem by dividing 100 by 25 first. Let’s see that. Cool, huh? Both ways work so you have a choice.**Please work these problems showing all steps.**1. 2. 3. 4. 1. 2. 3. 4. Anything we need to go back over before we continue?**Good job! Now, work these problems showing all steps.**5. 6. 7. 8. 5. 6. 7. 8.**How do I simplify a square root?**Now, practice by completing your worksheet.