Properties of Radicals

Radicals

How To Simplify

The purpose is to factor out a perfect square.

Perfect squares like 4, 9, 16, 25, 36, 49.... come out to whole numbers when their square roots are taken. To simplify we want to break apart into factors that include at least one perfect square. Then this number can leave the square root (evaluate).

Some text here about the topic of discussion

Multiple Choice

Simplify: $$\sqrt[]{48}$$  

• $$3\sqrt[]{6}$$  

• $$4\sqrt[]{3}$$  

• $$6\sqrt[]{6}$$  

• 14

Multiple Choice

Simplify: $$\sqrt[]{192}$$  

• $$8\sqrt[]{5}$$  

• $$3\sqrt[]{3}$$  

• $$8\sqrt[]{3}$$  

• $$4\sqrt[]{2}$$  

Multiple Choice

Simplify: $$\sqrt[]{80}$$  

• $$5\sqrt[]{7}$$  

• $$4\sqrt[]{5}$$  

• $$7\sqrt[]{5}$$  

• 10

Multiple Choice

Simplify: $$\sqrt[]{28}$$  

• $$2\sqrt[]{7}$$  

• $$3\sqrt[]{7}$$  

• 14

• $$8\sqrt[]{5}$$  

Multiplying Radicals

Think like terms! Square roots multiply with square roots. Regular numbers get multiplied with regular numbers. Check the product for simplifying.

Subject | Subject

Some text here about the topic of discussion

Multiple Choice

$$\sqrt[]{15}\cdot4\sqrt[]{3}$$  

• $$12\sqrt[]{5}$$  

• $$3\sqrt[]{5}$$  

• 45

• $$3\sqrt[]{2}$$  

Multiple Choice

$$\sqrt[]{10}\cdot\sqrt[]{10}$$  

• 10

• $$4\sqrt[]{30}$$  

• 100

• $$2\sqrt[]{5}$$  

Multiple Choice

$$3\sqrt[]{20}\cdot3\sqrt[]{20}$$  

• $$24\sqrt[]{10}$$  

• 20

• 40

• 180

Multiple Choice

$$\left(2\sqrt[]{6}\right)^2$$  

• $$2\sqrt[]{3}$$  

• 6

• 12

• 24

Rationalizing the Denominator

The objective is to have no square roots in the denominator. To do that we perform multiplication to the ratio that will remove the square root (cancel it) from the denominator.

Subject | Subject

Multiple Choice

Simplify: $$\frac{2}{\sqrt[]{2}}$$  

• $$\sqrt[]{2}$$  

• $$\frac{15}{5}$$  

• $$\frac{2\sqrt[]{5}}{3}$$  

• $$\frac{\sqrt[]{2}}{2}$$  

Multiple Choice

Simplify: $$\frac{\sqrt[]{2}}{4\sqrt[]{3}}$$  

• $$\frac{\sqrt[]{15}}{9}$$  

• $$\frac{2\sqrt[]{3}}{3}$$  

• $$\frac{\sqrt[]{6}}{12}$$  

• $$2\sqrt[]{6}$$