Question

3 prepare with calcchat simplifying square roots example 1 simplify √8. √8 = √4·2 = √4·√2 = 2√2 factor using the greatest perfect - square factor product property of square roots simplify example 2 simplify √(7/36). √(7/36) = √7/√36 = √7/6 quotient property of square roots simplify simplify the expression. 1. √27 2 -√112 3. √(11/64) 4. √(147/100) 5. √(18/49) 6. -√(65/121) 7. -√80 8. √32

Explanation:

Step1: Factor using greatest perfect - square factor for $\sqrt{27}$

$\sqrt{27}=\sqrt{9\times3}=\sqrt{9}\times\sqrt{3}$

Step2: Simplify

$ = 3\sqrt{3}$

Step3: Factor using greatest perfect - square factor for $-\sqrt{112}$

$-\sqrt{112}=-\sqrt{16\times7}=-\sqrt{16}\times\sqrt{7}$

Step4: Simplify

$=-4\sqrt{7}$

Step5: Use quotient property for $\sqrt{\frac{11}{64}}$

$\sqrt{\frac{11}{64}}=\frac{\sqrt{11}}{\sqrt{64}}$

Step6: Simplify

$=\frac{\sqrt{11}}{8}$

Step7: Use quotient property for $\sqrt{\frac{147}{100}}$

$\sqrt{\frac{147}{100}}=\frac{\sqrt{147}}{\sqrt{100}}$

Step8: Factor $\sqrt{147}$

$\sqrt{147}=\sqrt{49\times3}=\sqrt{49}\times\sqrt{3}=7\sqrt{3}$

Step9: Simplify the fraction

$\frac{\sqrt{147}}{\sqrt{100}}=\frac{7\sqrt{3}}{10}$

Step10: Use quotient property for $\sqrt{\frac{18}{49}}$

$\sqrt{\frac{18}{49}}=\frac{\sqrt{18}}{\sqrt{49}}$

Step11: Factor $\sqrt{18}$

$\sqrt{18}=\sqrt{9\times2}=\sqrt{9}\times\sqrt{2}=3\sqrt{2}$

Step12: Simplify the fraction

$\frac{\sqrt{18}}{\sqrt{49}}=\frac{3\sqrt{2}}{7}$

Step13: Use quotient property for $-\sqrt{\frac{65}{121}}$

$-\sqrt{\frac{65}{121}}=-\frac{\sqrt{65}}{\sqrt{121}}$

Step14: Simplify

$=-\frac{\sqrt{65}}{11}$

Step15: Factor using greatest perfect - square factor for $-\sqrt{80}$

$-\sqrt{80}=-\sqrt{16\times5}=-\sqrt{16}\times\sqrt{5}$

Step16: Simplify

$=-4\sqrt{5}$

Step17: Factor using greatest perfect - square factor for $\sqrt{32}$

$\sqrt{32}=\sqrt{16\times2}=\sqrt{16}\times\sqrt{2}$

Step18: Simplify

$=4\sqrt{2}$

Answer:

1. $3\sqrt{3}$
2. $-4\sqrt{7}$
3. $\frac{\sqrt{11}}{8}$
4. $\frac{7\sqrt{3}}{10}$
5. $\frac{3\sqrt{2}}{7}$
6. $-\frac{\sqrt{65}}{11}$
7. $-4\sqrt{5}$
8. $4\sqrt{2}$