9.2 Simplify square roots  (Page 3/3)

$\sqrt{27}$

$\sqrt{80}$

$\sqrt{125}$

$\sqrt{96}$

$\sqrt{200}$

$\sqrt{147}$

$\sqrt{450}$

$\sqrt{252}$

$\sqrt{800}$

$\sqrt{288}$

$\sqrt{675}$

$\sqrt{1250}$

$\sqrt{x^7}$

$\sqrt{y^{11}}$

$\sqrt{p^3}$

$\sqrt{q^5}$

$\sqrt{m^{13}}$

$\sqrt{n^{21}}$

$\sqrt{r^{25}}$

$\sqrt{s^{33}}$

$\sqrt{49n^{17}}$

$\sqrt{25m^9}$

$\sqrt{81r^{15}}$

$\sqrt{100s^{19}}$

$\sqrt{98m^5}$

$\sqrt{32n^{11}}$

$\sqrt{125r^{13}}$

$\sqrt{80s^{15}}$

$\sqrt{200p^{13}}$

$\sqrt{128q^3}$

$\sqrt{242m^{23}}$

$\sqrt{175n^{13}}$

$\sqrt{147m^7{n}^{11}}$

$\sqrt{48m^7{n}^5}$

$\sqrt{75r^{13}{s}^9}$

$\sqrt{96r^3{s}^3}$

$\sqrt{300p^9{q}^{11}}$

$\sqrt{192q^3{r}^7}$

$\sqrt{242m^{13}{n}^{21}}$

$\sqrt{150m^9{n}^3}$

$5+\sqrt{12}$

$8+\sqrt{96}$

$1+\sqrt{45}$

$3+\sqrt{125}$

$\frac{10-\sqrt{24}}{2}$

$\frac{8-\sqrt{80}}{4}$

$\frac{3+\sqrt{90}}{3}$

$\frac{15+\sqrt{75}}{5}$

$\sqrt{\frac{49}{64}}$

$\sqrt{\frac{100}{36}}$

$\sqrt{\frac{121}{16}}$

$\sqrt{\frac{144}{169}}$

$\sqrt{\frac{72}{98}}$

$\sqrt{\frac{75}{12}}$

$\sqrt{\frac{45}{125}}$

$\sqrt{\frac{300}{243}}$

$\sqrt{\frac{x^{10}}{x^6}}$

$\sqrt{\frac{p^{20}}{p^{10}}}$

$\sqrt{\frac{y^4}{y^8}}$

$\sqrt{\frac{q^8}{q^{14}}}$

$\sqrt{\frac{200x^7}{2x^3}}$

$\sqrt{\frac{98y^{11}}{2y^5}}$

$\sqrt{\frac{96p^9}{6p}}$

$\sqrt{\frac{108q^{10}}{3q^2}}$

$\sqrt{\frac{36}{35}}$

$\sqrt{\frac{144}{65}}$

$\sqrt{\frac{20}{81}}$

$\sqrt{\frac{21}{196}}$

$\sqrt{\frac{96x^7}{121}}$

$\sqrt{\frac{108y^4}{49}}$

$\sqrt{\frac{300m^5}{64}}$

$\sqrt{\frac{125n^7}{169}}$

$\sqrt{\frac{98r^5}{100}}$

$\sqrt{\frac{180s^{10}}{144}}$

$\sqrt{\frac{28q^6}{225}}$

$\sqrt{\frac{150r^3}{256}}$

$\sqrt{\frac{75r^9}{s^8}}$

$\sqrt{\frac{72x^5}{y^6}}$

$\sqrt{\frac{28p^7}{q^2}}$

$\sqrt{\frac{45r^3}{s^{10}}}$

$\sqrt{\frac{100x^5}{36x^3}}$

$\sqrt{\frac{49r^{12}}{16r^6}}$

$\sqrt{\frac{121p^5}{81p^2}}$

$\sqrt{\frac{25r^8}{64r}}$

$\sqrt{\frac{32x^5{y}^3}{18x^{3}y}}$

$\sqrt{\frac{75r^6{s}^8}{48r{s}^4}}$

$\sqrt{\frac{27p^{2}q}{108p^5{q}^3}}$

$\sqrt{\frac{50r^5{s}^2}{128r^2{s}^5}}$

1. ⓐ Elliott decides to construct a square garden that will take up 288 square feet of his yard. Simplify $\sqrt{288}$ to determine the length and the width of his garden. Round to the nearest tenth of a foot.
2. ⓑ Suppose Elliott decides to reduce the size of his square garden so that he can create a 5-foot-wide walking path on the north and east sides of the garden. Simplify $\sqrt{288}-5$ to determine the length and width of the new garden. Round to the nearest tenth of a foot.

1. ⓐ Melissa accidentally drops a pair of sunglasses from the top of a roller coaster, 64 feet above the ground. Simplify $\sqrt{\frac{64}{16}}$ to determine the number of seconds it takes for the sunglasses to reach the ground.
2. ⓑ Suppose the sunglasses in the previous example were dropped from a height of 144 feet. Simplify $\sqrt{\frac{144}{16}}$ to determine the number of seconds it takes for the sunglasses to reach the ground.

Explain why $\sqrt{x^4}=x^2$ . Then explain why $\sqrt{x^{16}}=x^8$ .

Explain why $7+\sqrt{9}$ is not equal to $\sqrt{7+9}$ .