4.3 simplifying square roots

• Wiskunde
• Middelbare school
• havo, vwo
• Leerjaar 2

Today

I am able to use the rule for multiplying
roots to simplify expressions.

The rule

$$\sqrt{a}\cdot \sqrt{b}=\sqrt{a\cdot b}$$

Calculate
You can use a capital v to indicate a square root here.

$$\sqrt{a}\cdot \sqrt{b}=\sqrt{a\cdot b}$$

$$\sqrt{12}\cdot \sqrt{3}$$

Calculate
You can use a capital v to indicate a square root here.

$$\sqrt{a}\cdot \sqrt{b}=\sqrt{a\cdot b}$$

$$\sqrt{15}\cdot 3\sqrt{3}\cdot \sqrt{5}$$

Calculate
You can use a capital v to indicate a square root here.

$$\sqrt{a}\cdot \sqrt{b}=\sqrt{a\cdot b}$$

$${(4\sqrt{3})}^2$$

Simplifying fractions by factorising

Let's observe

$$\sqrt{75}$$

Simplifying fractions by factorising

Let's observe

also

$$\sqrt{75}$$

$$75=5\cdot 15$$

$$75=3\cdot 25$$

Simplifying fractions by factorising

Let's observe

so 

is this progress?

$$\sqrt{75}$$

$$75=5\cdot 15$$

$$\sqrt{75}=\sqrt{5}\cdot \sqrt{15}$$

Simplifying fractions by factorising

Let's observe

so 

Is this progress? Why?

$$\sqrt{75}$$

$$75=3\cdot 25$$

$$\sqrt{75}=\sqrt{3}\cdot \sqrt{25}$$

Simplifying fractions by factorising

Let's observe

so 

Is this progress? Why?

Yes, because 

$$\sqrt{75}$$

$$75=3\cdot 25$$

$$\sqrt{75}=\sqrt{3}\cdot \sqrt{25}$$

$$\sqrt{3}\cdot \sqrt{25}=\sqrt{3}\cdot 5=5\sqrt{3}$$

Simplify
You can use a capital v to indicate a square root here.

$$\sqrt{a}\cdot \sqrt{b}=\sqrt{a\cdot b}$$

$$\sqrt{200}$$

Do the things