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1.4 B simplifying square roots

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Slide 1: Slide

WiskundeMiddelbare schoolhavo, vwoLeerjaar 2

This lesson contains 20 slides, with interactive quizzes and text slides.

Lesson duration is: 50 min

Items in this lesson

Slide 1 - Slide

Slide 2 - Slide

Today

You use the rule for multiplying
roots to simplify expressions.

You can rewrite fractions to bring
square roots form the denominator to
the numerator.

Slide 3 - Slide

How are you today?

😒🙁😐🙂😃

Slide 4 - Poll

The rule

\sqrt ​ a ​ ​ ​ \cdot \sqrt ​ b ​ ​ ​ = \sqrt ​ a \cdot b ​ ​ ​

Slide 5 - Slide

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 ​ ​ ​

Slide 6 - Open question

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 \sqrt ​ 3 ​ ​ ​ \cdot \sqrt ​ 5 ​ ​ ​

Slide 7 - Open question

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

\sqrt ​ a ​ ​ ​ \cdot \sqrt ​ b ​ ​ ​ = \sqrt ​ a \cdot b ​ ​ ​

(\sqrt ​ 3 ​ ​ ​)^{​ 2 ​ ​}

Slide 8 - Open question

Simplifying roots by factorising

Let's observe

\sqrt ​ 75 ​ ​ ​

Slide 9 - Slide

Simplifying roots by factorising

Let's observe

also

\sqrt ​ 75 ​ ​ ​

75 = 5 \cdot 15

75 = 3 \cdot 25

Slide 10 - Slide

Simplifying roots by factorising

Let's observe

so

is this progress?

\sqrt ​ 75 ​ ​ ​

75 = 5 \cdot 15

\sqrt ​ 75 ​ ​ ​ = \sqrt ​ 5 ​ ​ ​ \cdot \sqrt ​ 15 ​ ​ ​

Slide 11 - Slide

Simplifying roots by factorising

Let's observe

so

Is this progress? Why?

\sqrt ​ 75 ​ ​ ​

75 = 3 \cdot 25

\sqrt ​ 75 ​ ​ ​ = \sqrt ​ 3 ​ ​ ​ \cdot \sqrt ​ 25 ​ ​ ​

Slide 12 - Slide

Simplifying roots 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 ​ ​ ​

Slide 13 - Slide

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

\sqrt ​ a ​ ​ ​ \cdot \sqrt ​ b ​ ​ ​ = \sqrt ​ a \cdot b ​ ​ ​

\sqrt ​ 200 ​ ​ ​

Slide 14 - Open question

Simplifying fractions by factorising

Let's observe

As a rule, we don't like to have roots in the denominator of our fractions. Luckily, there's a way to move the square root.

\frac{​ 1 ​ ​}{​ \sqrt ​ 2 ​ ​ ​ ​}

Slide 15 - Slide

Simplifying fractions by factorising

\frac{​ 1 ​ ​}{​ \sqrt ​ 2 ​ ​ ​ ​} \cdot 1

Slide 16 - Slide

Simplifying fractions by factorising

\frac{​ 1 ​ ​}{​ \sqrt ​ 2 ​ ​ ​ ​} \cdot 1 =

\frac{​ 1 ​ ​}{​ \sqrt ​ 2 ​ ​ ​ ​} \cdot \frac{​ \sqrt ​ 2 ​ ​ ​ ​ ​}{​ \sqrt ​ 2 ​ ​ ​ ​} =

Slide 17 - Slide

Simplifying fractions by factorising

\frac{​ 1 ​ ​}{​ \sqrt ​ 2 ​ ​ ​ ​} \cdot 1 =

\frac{​ 1 ​ ​}{​ \sqrt ​ 2 ​ ​ ​ ​} \cdot \frac{​ \sqrt ​ 2 ​ ​ ​ ​ ​}{​ \sqrt ​ 2 ​ ​ ​ ​} =

\frac{​ 1 ​ ​}{​ \sqrt ​ 2 ​ ​ ​ ​} \cdot \frac{​ \sqrt ​ 2 ​ ​ ​ ​ ​}{​ \sqrt ​ 2 ​ ​ ​ ​} = \frac{​ \sqrt ​ 2 ​ ​ ​ ​ ​}{​ \sqrt ​ 2 ​ ​ ​ \cdot \sqrt ​ 2 ​ ​ ​ ​} = \frac{​ \sqrt ​ 2 ​ ​ ​ ​ ​}{​ \sqrt ​ 4 ​ ​ ​ ​}

Slide 18 - Slide

Simplifying fractions by factorising

\frac{​ 1 ​ ​}{​ \sqrt ​ 2 ​ ​ ​ ​} \cdot 1 =

\frac{​ 1 ​ ​}{​ \sqrt ​ 2 ​ ​ ​ ​} \cdot \frac{​ \sqrt ​ 2 ​ ​ ​ ​ ​}{​ \sqrt ​ 2 ​ ​ ​ ​} =

\frac{​ 1 ​ ​}{​ \sqrt ​ 2 ​ ​ ​ ​} \cdot \frac{​ \sqrt ​ 2 ​ ​ ​ ​ ​}{​ \sqrt ​ 2 ​ ​ ​ ​} = \frac{​ \sqrt ​ 2 ​ ​ ​ ​ ​}{​ \sqrt ​ 2 ​ ​ ​ \cdot \sqrt ​ 2 ​ ​ ​ ​} = \frac{​ \sqrt ​ 2 ​ ​ ​ ​ ​}{​ \sqrt ​ 4 ​ ​ ​ ​} = \frac{​ \sqrt ​ 2 ​ ​ ​ ​ ​}{​ 2 ​} (= \frac{​ 1 ​ ​}{​ 2 ​} \sqrt ​ 2 ​ ​ ​)

Slide 19 - Slide

Do the things

Slide 20 - Slide

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