Roots and Radicals

$5x+y=2$

        $2=x$

In the following exercises, simplify using absolute value signs as needed. $\sqrt{175n^{13}},\sqrt[5]{512p^5},\sqrt[4]{324q^7}$

Graph the quadratic function $f \left(x\right) = 2x^2 - 4x - 3$ first using the properties as we

did in the last section and then graph it using transformations. Which method do you prefer? Why?

Simplify: $\left(a\right)-\sqrt{64} \left(b\right)\sqrt{225}$

Simplify: $\left(a\right)\sqrt{100}$ 

$\left(b\right)-\sqrt{121}$

Simplify: $\left(a\right) \sqrt{-169}$    $\left(b\right)-\sqrt{81}$

Simplify: $\left(a\right) -\sqrt{49}$    $\left(b\right)\sqrt{-121}$

Simplify: $\left(a\right) \sqrt[3]{27} \left(b\right) \sqrt[4]{256} \left(c\right) \sqrt[5]{243}$

Simplify: $\left(a\right) \sqrt[3]{1000} \left(b\right) \sqrt[4]{16} \left(c\right) \sqrt[5]{243}$

Simplify: $\left(a\right) \sqrt[3]{-27} \left(b\right) \sqrt[4]{-256} \left(c\right)\sqrt[5]{-32}$

Simplify: $\left(a\right)\sqrt[3]{-216} \left(b\right)\sqrt[4]{-81} \left(c\right)\sqrt[5]{1024}$

Estimate each root between two consecutive whole numbers: $\left(a\right) \sqrt{38} \left(b\right) \sqrt[3]{93}$

Estimate each root between two consecutive whole numbers: $\left(a\right) \sqrt{84} \left(b\right)\sqrt[3]{152}$

Round to two decimal places:

$\left(a\right)\sqrt{11} \left(b\right)\sqrt[3]{71} \left(c\right)\sqrt[4]{127}$

Round to two decimal places: $\left(a\right)\sqrt{13} \left(b\right)\sqrt[3]{84} \left(c\right)\sqrt[4]{98}$

Simplify: $\left(a\right)\sqrt{b^2} \left(b\right)\sqrt[3]{3^3} \left(c\right)\sqrt[4]{m^4} \left(d\right)\sqrt[5]{q^5}$

Simplify: $\left(a\right) \sqrt{y^2} \left(b\right) \sqrt[3]{p^3} \left(c\right) \sqrt[4]{z^4} \left(d\right) \sqrt[5]{q^5}$

Simplify: $\left(a\right) \sqrt{y^{18}} \left(b\right) \sqrt{z^{12}}$

Simplify: $\left(a\right) \sqrt{m^4} \left(b\right) \sqrt{b^{10}}$

Simplify: $\left(a\right) \sqrt[4]{u^{12}} \left(b\right) \sqrt[3]{v^{15}}$

Simplify: $\left(a\right) \sqrt[5]{c^{20}} \left(b\right)\sqrt[6]{d^{24}}$

Simplify: $\left(a\right) \sqrt{64x^2} \left(b\right) -\sqrt{100p^2}$

Simplify: $\left(a\right) \sqrt{169y^2} \left(b\right)-\sqrt{121y^2}$

Simplify: $\left(a\right) \sqrt[3]{27x^{27}} \left(b\right)\sqrt[4]{81q^{28}}$

Simplify: $\left(a\right) \sqrt[3]{125q^9} \left(b\right) \sqrt[5]{243q^{25}}$

Simplify: $\left(a\right) \sqrt{100a^2{b}^2} \left(b\right)\sqrt{144p^{12}{q}^{20}} \left(c\right) \sqrt[3]{8x^{30}{y}^{12}}$

Simplify: $\left(a\right) \sqrt{225m^2{n}^2} \left(b\right)\sqrt{169x^{10}{y}^{14}} \left(c\right)\sqrt[3]{27w^{36}{z}^{15}}$

In the following exercises, simplify. 

ⓐ $\sqrt{64}$ ⓑ $-\sqrt{81}$ 

Simplify the given value.

.ⓐ $\sqrt{169}$ ⓑ $-\sqrt{100}$ 

Simplify the given value.

ⓐ $\sqrt{196}$ ⓑ $-\sqrt{ 1}$ 

Simplify Expressions 

ⓐ $\sqrt{144}$ ⓑ $-\sqrt{ 121 }$

Simplify Expressions with Roots.

ⓐ $\sqrt{\frac{4}{9}}$  ⓑ $-\sqrt{0.01}$ 

ⓐ $\sqrt{\frac{64}{121}}$ ⓑ $-\sqrt{0.04}$

In the following exercise, simplify. 

$ⓐ \sqrt{-121} ⓑ - \sqrt{289}$

In the following exercises, simplify 

ⓐ $-\sqrt{400}$ⓑ $\sqrt{-36}$ 

ⓐ $-\sqrt{225}$ ⓑ $\sqrt{-9}$ 

In the following exercises, simplify. 

ⓐ $\sqrt{-49}$ ⓑ $-\sqrt{ 256 }$

In the following exercises, simplify. 

$\left(a\right)\sqrt[3]{216}\left(b\right)\sqrt[4]{256}$

In the following exercises, simplify. 

$\left(a\right)\sqrt[3]{27}\left(b\right)\sqrt[4]{16}\left(c\right)\sqrt[5]{243}$

In the following exercises, simplify. 

$\left(a\right)\sqrt[3]{512}\left(b\right)\sqrt[4]{81}\left(c\right)\sqrt[5]{1}$

In the following exercises, simplify. 

$\left(a\right)\sqrt[3]{125}\left(b\right)\sqrt[4]{1296}\left(c\right)\sqrt[5]{1024}$

In the following exercises, simplify. 

$\left(a\right)\sqrt[3]{-8}\left(b\right)\sqrt[4]{-81}\left(c\right)\sqrt[5]{-32}$

In the following exercise, simplify. 

(a) $\sqrt[3]{-64}$

(b) $\sqrt[4]{-16}$

(c) $\sqrt[5]{-243}$

In the following exercises, simplify. 

$$\begin{gathered} \left(a\right)\sqrt[3]{-125} \\ \left(b\right)\sqrt[4]{-1296} \\ \left(c\right)\sqrt[5]{-1024} \end{gathered}$$

In the following exercises, simplify. 

$$\begin{gathered} \left(a\right)\sqrt[3]{-512} \\ \left(b\right)\sqrt[4]{-81} \\ \left(c\right)\sqrt[5]{-1} \end{gathered}$$

In the following exercises, estimate each root between two consecutive whole numbers. 

ⓐ $\sqrt{70}$ ⓑ $\sqrt[3]{71}$ 

In the following exercises, estimate each root between two consecutive whole numbers. 

ⓐ $\sqrt{55}$ ⓑ $\sqrt[3]{119}$ 

In the following exercises, estimate each root between two consecutive whole numbers. 

ⓐ  $\sqrt{200}$ⓑ $\sqrt[3]{137}$

In the following exercises, estimate each root between two consecutive whole numbers. 

ⓐ $\sqrt{172}$ ⓑ $\sqrt[3]{200 }$

In the following exercises, approximate each root and round to two decimal places. 

ⓐ $\sqrt{19}$ ⓑ $\sqrt[3]{89}$ 3 ⓒ $\sqrt[4]{ 97 }$