Section 1
Simplify Expressions with Roots
In the following exercises, simplify.(a) $\sqrt{64}$ (b) $-\sqrt{81}$
In the following exercises, simplify. (b) $\sqrt{169}$ (b) $-\sqrt{100}$
In the following exercises, simplify.(C) $\sqrt{196}$ (C) $-\sqrt{1}$
In the following exercises, simplify. (a) $\sqrt{144}$ (b) $-\sqrt{121}$
In the following exercises, simplify. $\sqrt{\frac{4}{9}}$ (b) $-\sqrt{0.01}$
In the following exercises, simplify. (a) $\sqrt{\frac{64}{121}}$ (.) $-\sqrt{0.16}$
In the following exercises, simplify.(a) $\sqrt{-121}$ (b) $-\sqrt{289}$
In the following exercises, simplify.(6) $-\sqrt{400}$ (b) $\sqrt{-36}$
In the following exercises, simplify.a) $-\sqrt{225}$ (b) $\sqrt{-9}$
In the following exercises, simplify. (a) $\sqrt{-49}$ (b) $-\sqrt{256}$
In the following exercises, simplify..(a) $\sqrt[3]{216}$ (b) $\sqrt[4]{256}$
In the following exercises, simplify.(a) $\sqrt[3]{27}$ (b) $\sqrt[4]{16}$ (c) $\sqrt[5]{243}$
In the following exercises, simplify. (a) $\sqrt[3]{512}$ (b) $\sqrt[4]{81}$ (c) $\sqrt[5]{1} \quad$
In the following exercises, simplify.(a) $\sqrt[3]{125}$ (b) $\sqrt[4]{1296}$ (c) $\sqrt[5]{1024} \quad$
In the following exercises, simplify.(a) $\sqrt[3]{-8}$ (b) $\sqrt[4]{-81}$ (c) $\sqrt[5]{-32}$
In the following exercises, simplify.
(a) $\sqrt[3]{-64}$(b) $\sqrt[4]{-16}$(c) $\sqrt[5]{-243}$
(a) $\sqrt[3]{-125}$(6) $\sqrt[4]{-1296}$(c) $\sqrt[5]{-1024}$
(a) $\sqrt[3]{-512}$(b) $\sqrt[4]{-81}$(c) $\sqrt[5]{-1}$
In the following exercises, estimate eoch raot between two cansecutive whole numbers..(a) $\sqrt{70}$ (b) $\sqrt[3]{71}$
In the following exercises, estimate eoch raot between two cansecutive whole numbers. (a) $\sqrt{55}$ (b) $\sqrt[3]{119}$
In the following exercises, estimate eoch raot between two cansecutive whole numbers. (a) $\sqrt{200}$ (b) $\sqrt[3]{137}$
In the following exercises, estimate eoch raot between two cansecutive whole numbers.(a) $\sqrt{172}$ (b) $\sqrt[3]{200}$
In the following exercises, approximate each root and round to wo decimal places.(a) $\sqrt{19}$ (b) $\sqrt[3]{89}$ (c) $4 \sqrt{97}$
In the following exercises, approximate each root and round to wo decimal places. (a) $\sqrt{21}$ (b) $\sqrt[3]{93}$ (c) $\sqrt[4]{101}$
In the following exercises, approximate each root and round to wo decimal places.. (a) $\sqrt{53}$ (b) $\sqrt[3]{147}$ (c) $\sqrt[4]{452}$
In the following exercises, approximate each root and round to wo decimal places. (a) $\sqrt{47}$ (b) $\sqrt[3]{163}$ (c) $\sqrt[4]{527}$
In the foflowing exercises, simplify using absolute volues as necessary.(a) $\sqrt[5]{u^5}$ (b) $\sqrt[8]{v^8}$
In the foflowing exercises, simplify using absolute volues as necessary.(a) $\sqrt[3]{a^3}$ (b) $\sqrt[9]{b^9}$
In the foflowing exercises, simplify using absolute volues as necessary..(a) $\sqrt[4]{y^4}$ (b) $\sqrt[7]{m^7}$
In the foflowing exercises, simplify using absolute volues as necessary.(a) $\sqrt[5]{k^8}$ (b) $\sqrt[6]{p^6}$
In the foflowing exercises, simplify using absolute volues as necessary. (a) $\sqrt{x^6}$ (b) $\sqrt{y^{16}}$
In the foflowing exercises, simplify using absolute volues as necessary. (a) $\sqrt{a^{14}}$ (b) $\sqrt{w^{24}}$
In the foflowing exercises, simplify using absolute volues as necessary. (a) $\sqrt{x^{24}}$ (b) $\sqrt{y^{22}}$
In the foflowing exercises, simplify using absolute volues as necessary. (a) $\sqrt{a^{12}}$ (b) $\sqrt{b^{26}}$
In the foflowing exercises, simplify using absolute volues as necessary.(a) $\sqrt[3]{x^9}$ (b) $\sqrt[4]{y^{12}}$
In the foflowing exercises, simplify using absolute volues as necessary.(a) $\sqrt[5]{a^{10}}$ (b) $\sqrt[3]{b^{27}}$
In the foflowing exercises, simplify using absolute volues as necessary.(a) $\sqrt[4]{m^8}$ (b) $\sqrt[5]{n^{20}}$
In the foflowing exercises, simplify using absolute volues as necessary.(a) $\sqrt[5]{r^{12}}$ (b) $\sqrt[3]{s^{30}}$
In the foflowing exercises, simplify using absolute volues as necessary. (a) $\sqrt{49 x^2}$ (b) $-\sqrt{81 x^{18}}$
In the foflowing exercises, simplify using absolute volues as necessary. (a) $\sqrt{100 y^2}$ (b) $-\sqrt{100 m^{32}}$
In the foflowing exercises, simplify using absolute volues as necessary.(a) $\sqrt{121 m^{20}}$ (b) $-\sqrt{64 a^2}$
In the foflowing exercises, simplify using absolute volues as necessary.
(a) $\sqrt{81 x^{36}}$(b) $-\sqrt{25 x^2}$
(a) $\sqrt[4]{16 x^8}$(b) $\sqrt[6]{64 y^{12}}$
(a) $\sqrt[3]{-8 c^9}$(b) $\sqrt[3]{125 d^{15}}$
(a) $\sqrt[3]{216 a^6}$(b) $\sqrt[5]{32 b^{20}}$
(a) $\sqrt[7]{128 r^{14}}$(6) $\sqrt[4]{81 s^{24}}$
(a) $\sqrt{144 x^2 y^2}$(b) $\sqrt{169 w^8 y^{10}}$(c) $\sqrt[3]{8 a^{51} b^6}$
(a) $\sqrt{196 a^2 b^2}$(b) $\sqrt{81 p^{24} q^6}$(c) $\sqrt[3]{27 p^{45} q^9}$
(a) $\sqrt{121 a^2 b^2}$(B) $\sqrt{9 c^8 d^{12}}$(c) $\sqrt[3]{64 x^{15} y^{66}}$
(a) $\sqrt{225 x^2 y^2 z^2}$(b) $\sqrt{36 r^6 s^{20}}$(c) $\sqrt[3]{125 y^{18} z^{27}}$
Why is there no real number equal to $V-64$ ?
What is the difference between $9^2$ and $\sqrt{9}$ ?
Explain what is meant by the $n^{\text {th }}$ root of a number.
Explain the difference of finding the $n^{\text {h }}$ root of a number when the index is even compared to when the index is odd.