Add Math Y10 C3 Surds and Radicals

C3 Surds and Radicles

By Kewin Aljoe

Introducing Surds and Radicals

What does this image show?

Lesson outcomes

• To understand surds and radicals

• To be able to multiply and divide surds

• To be able to simplify basic surds

Multiple Select

Which of these are Radicals?

• √81

• √ 1

• √48

• √100

Multiple Select

Which of these are Surds?

• √81

• √ 1

• √48

• √100

Multiple Choice

$$\sqrt{3}\times\sqrt{8}$$  

• $$\sqrt{24}$$  

• $$\sqrt{42}$$  

• $$7$$  

• 24

Multiple Choice

Do you remember addition with surds?

(It is the same as Like Terms.)

3e + 4e + 2f

• 7e + 2f

• 9ef 

• 12e + 2f 

Multiple Choice

Do you remember addition with surds?

(It is the same as Like Terms.)

$$3\sqrt[]{3}+4\sqrt[]{3}+5\sqrt[]{2}=$$  

• $$7\sqrt[]{3}+5\sqrt[]{2}$$  

• $$12\sqrt[]{6}$$  

• $$12\sqrt[]{8}$$  

Multiple Choice

$$\sqrt{7}\times\sqrt{4}$$  

• $$\sqrt{28}$$  

• $$\sqrt{24}$$  

• $$\sqrt{11}$$  

• 28

Expanding Brackets Surds

Multiple Choice

Expand and simplify.....

√5(1 - √3)

• √5 - √15

• 1√5 - 3√5

• √5 - 3√5

• √5 - 5√3

Multiple Choice

​Multiplying surds also works the same as algebra.

$$4x\times5y=$$  

• $$20xy$$  

• $$9xy$$  

• $$45xy$$  

Multiple Choice

Expand and simplify.....

√3(√2 + 4)

• √6 + 4√3

• √6 + 3√3

• 3√2 + 3√4

• 2√3 + 4√3

Multiple Choice

$$\sqrt{3}\times\sqrt{6}$$  

• $$\sqrt{18}$$  

• $$\sqrt{42}$$  

• $$\sqrt{9}$$  

• 3

Multiple Choice

Expand and simplify.....

√3(√2 + 4)

• √6 + 4√3

• √6 + 3√3

• 3√2 + 3√4

• 2√3 + 4√3

Multiple Choice

​Multiplying surds also works the same as algebra.

$$4\sqrt[]{3}\times5\sqrt[]{2}=$$  

• $$20\sqrt[]{6}$$  

• $$9\sqrt[]{5}$$  

• $$\sqrt[]{120}$$  

Multiple Choice

Expand and simplify ...

(3 + 2√2)(1 + 3√2)

• 15 + 11√2

• 15 + 5√2

• 5 + 11√2

• 5 + 5√2

Multiple Choice

Notice that the coefficients multiplied together.

What are the coefficients in this?

$$4\sqrt[]{3}\times5\sqrt[]{2}=$$  

• 4, 5 

• 4, 3 

• 3, 2 

• 3, 5

Multiple Choice

Expand and simplify ...

(2 + √2)(5 + √2)

• 12 + 7√2

• 12 + √2

• 12 + 10√2

• 14 + 7√2

Multiple Choice

Expand and simplify ...

(2 + √3)(3 - √3)

• 3 - 5√3

• 6 + √3

• 3 + √3

• 15 + 5√3

Multiple Choice

Multiply the coefficients together.

Multiply the roots together.

$$5\sqrt[]{2}\times7\sqrt[]{3}=$$  

• $$35\sqrt[]{6}$$  

• $$12\sqrt[]{6}$$  

• $$12\sqrt[]{5}$$  

• $$35\sqrt[]{5}$$  

Multiple Choice

Expand and simplify ...

(2 + √3)(1 + √3)

• 5 + 3√3

• 2 + 3√3

• 5 + √3

• 11 + 3√3

Poll

How many marks did you get?

• 0-2

• 3-4

• 5-6

• 7-8

Multiple Choice

Multiply the coefficients together.

Multiply the roots together.

$$3\sqrt[]{3}\times4\sqrt[]{2}=$$  

• $$7\sqrt[]{6}$$  

• $$12\sqrt[]{6}$$  

• $$12\sqrt[]{5}$$  

• $$7\sqrt[]{5}$$  

Multiple Choice

Don't forget to simplify your answers.

$$3\sqrt[]{2}\times\sqrt[]{2}=$$  

• $$12$$  

• $$3\sqrt[]{4}$$  

• $$7$$  

• $$\sqrt[]{12}$$  

• $$6$$  

Multiple Choice

$$\sqrt{36}\div\sqrt{9}$$  

• $$\sqrt{8}$$  

• $$\sqrt{2}$$  

• 2

• $$\sqrt{3}$$  

Multiple Choice

Don't forget to simplify your answers.

$$2\sqrt[]{6}\times3\sqrt[]{2}=$$  

• $$12\sqrt[]{3}$$  

• $$6\sqrt[]{12}$$  

• $$18\sqrt[]{2}$$  

• $$18\sqrt[]{3}$$  

Multiple Choice

$$\sqrt{54}\div\sqrt{6}$$  

• $$\sqrt{8}$$  

• $$\sqrt{2}$$  

• 3

• $$\sqrt{3}$$  

Multiple Choice

$$3\sqrt[]{5}\times2\sqrt[]{10}=30\sqrt[]{2}$$  

• TRUE

• FALSE

Multiple Select

$$\sqrt{54}\div\sqrt{6}$$  

• $$\sqrt{9}$$  

• $$\sqrt{3}$$  

• 3

• $$\sqrt{\frac{54}{6}}$$  

Multiple Choice

$$\sqrt[]{12}\times\sqrt[]{2}\times\sqrt[]{2}=3\sqrt[]{4}$$  

• TRUE

• FALSE

Multiple Choice

$$\sqrt{21}\div\sqrt{7}$$  

• 3

• $$\sqrt{3}$$  

• 21

• $$\sqrt{4}$$  

Multiple Choice

Dividing surds is similar. Try using the same ideas with this.

$$6\sqrt[]{15}\div2\sqrt[]{3}=$$  

• $$3\sqrt[]{5}$$  

• $$12\sqrt[]{45}$$  

• $$36\sqrt[]{5}$$  

• $$4\sqrt[]{5}$$  

Multiple Choice

$$\frac{\sqrt{15}}{\sqrt{3}}$$  

• 5

• $$\sqrt{12}$$  

• $$\sqrt{5}$$  

• $$\sqrt{3}$$  

Multiple Choice

Dividing surds is similar. Try using the same ideas with this.

Don't forget to simplify.

$$10\sqrt[]{20}\div2\sqrt[]{5}=$$  

• $$3\sqrt[]{5}$$  

• $$8\sqrt[]{5}$$   

• $$36\sqrt[]{5}$$  

• $$4\sqrt[]{5}$$  

• $$10$$  

Multiple Choice

Division can also be set out as a fraction.

$$\frac{8\sqrt[]{24}}{2\sqrt[]{12}}=$$  

• $$4\sqrt[]{2}$$  

• $$2\sqrt[]{4}$$  

• $$6\sqrt[]{6}$$  

Poll

How many marks did you get?

• 0-2

• 3-4

• 5-6

• 7-8