Simplifying Radicals

Simplifying Radicals

by Mr Salomon

​Simplifying Radicals

1. ​Radicals, in our case, square roots must be simplified as much as possible.

2. ​Simplifying radicals removes as many perfect squares or "pairs" as possible.

3. ​To simplify, break the radicand into factors.

4. ​Continue to factor until only prime numbers or perfect squares remain

5. ​Place "pairs" or perfect squares on the "outside"

6. ​Remember to multiply all coefficients together!

Multiple Choice

Simplify $$\sqrt[]{32}$$  

• $$\sqrt[]{32}$$  

• $$16\sqrt[]{2}$$  

• $$4\sqrt[]{2}$$  

• $$2\sqrt[]{8}$$  

Multiple Choice

Simplify $$\sqrt[]{50}$$  

• $$5\sqrt[]{2}$$  

• $$25\sqrt[]{2}$$  

• $$\sqrt[]{5\cdot10}$$  

• $$\sqrt[]{50}$$  

Multiple Choice

Simplify $$\sqrt[]{60}$$  

• $$2\sqrt[]{15}$$  

• $$2\sqrt[]{30}$$  

• $$30\sqrt[]{2}$$  

• $$\sqrt[]{6\cdot10}$$  

Multiple Choice

Simplify $$\sqrt[]{6}\cdot\sqrt[]{18}$$  

• $$6\sqrt[]{3}$$  

• $$3\sqrt[]{8}$$  

• $$6$$  

• $$2\sqrt[]{6}$$  

​Simplifying Radicals with Coefficients

Multiple Choice

Simplify $$3\sqrt[]{32}$$  

• $$12\sqrt[]{2}$$  

• $$7\sqrt[]{8}$$  

• $$4\sqrt[]{2}$$  

• $$12\sqrt[]{8}$$  

Multiple Choice

Simplify $$4\sqrt[]{450}$$  

• $$60\sqrt[]{2}$$  

• $$12\sqrt[]{2}$$  

• $$900\sqrt[]{2}$$  

• $$12\sqrt[]{50}$$  

Multiple Choice

HARDer - Simplify $$3x\sqrt[]{882x^5}$$  

• $$63x^2\sqrt[]{2x}$$  

• $$1323\sqrt[]{2x^5}$$  

• uh what?

• Just follow the same steps and look for "pairs"

Poll

How comfortable are you with simplifying radicals?

• I understand fully

• I am okay but will get it with more practice

• I can do it but I am not fast

• I am lost