Roots and Radicals Review

The "n" is the "index" and lets us know which root we're taking of "x". The stuff on the inside of the radical is called the "radicand". In this case, the radicand is x. Lastly, the value of the radical is the "nth" root of the radicand.

Recall the notation for radicals:

​To simplify radicals, we take the nth root of whatever we can. We leave the rest under the radical sign

​Lastly, with even roots (index is even). We have to be aware of the "principal root" rule and make sure our root stays positive.

Now, it's your turn to try. The remaining slides are all practice questions.

Fill in the Blank

Simplify the radical expression: $$\sqrt[3]{p^{12}}=$$

(you can use the ^ symbol to indicate an exponent. Ex: x^2 means $$x^2$$ )

Multiple Choice

Simplify the expression: $$\sqrt[4]{a^6}=$$

• $$a^4\cdot\sqrt[4]{a^2}$$

• $$\left|a\right|\cdot\sqrt[4]{a^2}$$

• $$a\cdot\sqrt[4]{a^2}$$

Fill in the Blank

$$\sqrt[4]{m^{16}}=$$

(you can use the ^ symbol to indicate an exponent. Ex: x^2 means $$x^2$$ )

Fill in the Blank

$$\sqrt[5]{x^{20}}=$$

(you can use the ^ symbol to indicate an exponent. Ex: x^2 means $$x^2$$ )

Fill in the Blank

$$\sqrt[6]{y^{18}}=$$

(you can use the ^ symbol to indicate an exponent. Ex: x^2 means $$x^2$$ )

Fill in the Blank

Simplify the following radical: $$\sqrt[]{\left(m+1\right)^4}=$$

(you can use the ^ symbol to indicate an exponent. Ex: x^2 means $$x^2$$ )

Fill in the Blank

Simplify the Radical Expression: $$\sqrt[5]{243x^{15}y^{20}}=$$

(you can use the ^ symbol to indicate an exponent. Ex: x^2 means $$x^2$$ )

Fill in the Blank

$$\sqrt[]{p^{10}}=$$

Multiple Choice

Simplify the following radical expression: $$\sqrt[3]{128x^5y^8}$$

• $$64x^3y^6\cdot\sqrt[3]{2x^2y^2}$$

• $$4xy^2\cdot\sqrt[3]{2x^2y^2}$$

• $$2\left|x\right|y^2\cdot\sqrt[]{4xy^2}$$

• $$4\left|x\right|y^2\cdot\sqrt[3]{2xy}$$

Multiple Choice

Simplify the following radical expression: $$\sqrt[]{60a^2b^3c^{11}}\ =$$

• $$15abc\cdot\sqrt[]{4bc^9}$$

• $$4abc^5\sqrt[]{15bc}$$

• $$2\left|a\right|bc^5\cdot\sqrt[]{15bc}$$

• $$2\left|abc^5\right|\cdot\sqrt[]{15bc^2}$$

Multiple Choice

Simplify the radical expression: $$\sqrt[6]{x^{12}y^{20}z^9}=$$

• $$x^2\left|y^3\right|z\cdot\sqrt[6]{y^2z^3}$$

• $$x^2y^3z^2$$

• $$x^2y^2z\cdot\sqrt[]{y^8z^3}$$

• $$x^2\left|y^3z\right|\cdot\sqrt[6]{yz^3}$$

Multiple Choice

Simplify: $$\sqrt[5]{30x^3y^9z^{15}\ }=$$

• $$yz^3\cdot\sqrt[5]{30x^3y^4}$$

• $$\left|yz^3\right|\cdot\sqrt[5]{30x^3y^3z}$$

• $$6yz^3\cdot\sqrt[5]{x^3y^4}$$

Multiple Choice

$$\sqrt[4]{162a^6b^{10}\ }=$$

• $$3ab\cdot\sqrt[4]{2a^2b^2}$$

• $$3\left|ab\right|\cdot\sqrt[4]{2a^2b^2}$$

• $$3\left|a\right|b^2\cdot\sqrt[4]{2a^2b^2}$$

• $$2a^4b^8\cdot\sqrt[]{81a^2b^2}$$