4.4 roots and powers

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Slide 1: Slide

WiskundeMiddelbare schoolhavo, vwoLeerjaar 2

This lesson contains 13 slides, with interactive quizzes and text slides.

Lesson duration is: 50 min

Items in this lesson

Slide 1 - Slide

Today

- I am able to simplify square roots of powers

- I am able to write expressions with fractions and roots as a power of x.

Slide 2 - Slide

Remember?

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

Slide 3 - Slide

We can simplify this:

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

\sqrt ​ x^{​ 20 ​ ​} ​ ​ ​

Slide 4 - Slide

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

\sqrt ​ x^{​ 20 ​ ​} ​ ​ ​ = \sqrt ​ (x^{​ 10 ​ ​})^{​ 2 ​ ​} ​ ​ ​

Slide 5 - Slide

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

\sqrt ​ x^{​ 20 ​ ​} ​ ​ ​ = \sqrt ​ (x^{​ 10 ​ ​})^{​ 2 ​ ​} ​ ​ ​ = x^{​ 10 ​ ​}

Slide 6 - Slide

or this one

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

\sqrt ​ x^{​ 9 ​ ​} ​ ​ ​

Slide 7 - Slide

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

\sqrt ​ x^{​ 9 ​ ​} ​ ​ ​ = \sqrt ​ x^{​ 8 ​ ​} \cdot x ​ ​ ​ = \sqrt ​ x^{​ 8 ​ ​} ​ ​ ​ \cdot \sqrt ​ x ​ ​ ​

Slide 8 - Slide

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

\sqrt ​ x^{​ 9 ​ ​} ​ ​ ​ = \sqrt ​ x^{​ 8 ​ ​} \cdot x ​ ​ ​ = \sqrt ​ x^{​ 8 ​ ​} ​ ​ ​ \cdot \sqrt ​ x ​ ​ ​ =

\sqrt ​ (x^{​ 4 ​ ​})^{​ 2 ​ ​} ​ ​ ​ \cdot \sqrt ​ x ​ ​ ​ = x^{​ 4 ​ ​} \cdot \sqrt ​ x ​ ​ ​ = x^{​ 4 ​ ​} \sqrt ​ x ​ ​ ​

Slide 9 - Slide

Simplify
Use a capital v for square roots and a ^ for powers.

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

\sqrt ​ 9 a^{​ 10 ​ ​} ​ ​ ​

Slide 10 - Open question

Do exercise 56.
Work in pairs.

Slide 11 - Open question

I'll show you how this works.

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

\frac{​ \sqrt ​ a ​ ​ ​ ​ ​}{​ \sqrt ​ b ​ ​ ​ ​} = \sqrt ​ \frac{​ a ​ ​}{​ b ​} ​ ​ ​

Slide 12 - Slide

Practice!

timer

10:00

Slide 13 - Slide

4.4 roots and powers

Items in this lesson

Slide 1 - Slide

Slide 2 - Slide

Slide 3 - Slide

Slide 4 - Slide

Slide 5 - Slide

Slide 6 - Slide

Slide 7 - Slide

Slide 8 - Slide

Slide 9 - Slide

Slide 10 - Open question

Slide 11 - Open question

Slide 12 - Slide

Slide 13 - Slide

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