Roots and like terms

Simplify

\sqrt ​ 32 ​ ​ ​

2 \sqrt ​ 6 ​ ​ ​

2 \sqrt ​ 4 ​ ​ ​

6 \sqrt ​ 2 ​ ​ ​

4 \sqrt ​ 2 ​ ​ ​

1 / 12

Slide 1: Quiz

WiskundeMiddelbare schoolvwoLeerjaar 2

This lesson contains 12 slides, with interactive quizzes and text slides.

Lesson duration is: 30 min

Items in this lesson

Simplify

\sqrt ​ 32 ​ ​ ​

2 \sqrt ​ 6 ​ ​ ​

2 \sqrt ​ 4 ​ ​ ​

6 \sqrt ​ 2 ​ ​ ​

4 \sqrt ​ 2 ​ ​ ​

Slide 1 - Quiz

Remember, you can either:

Separate into prime factors:

Find a factor that is a square number:

\sqrt ​ 32 ​ ​ ​ = \sqrt ​ 2 ​ ​ ​ \cdot \sqrt ​ 2 ​ ​ ​ \cdot \sqrt ​ 2 ​ ​ ​ \cdot \sqrt ​ 2 ​ ​ ​ \cdot \sqrt ​ 2 ​ ​ ​ = (\sqrt ​ 2 ​ ​ ​)^{​ 2 ​ ​} \cdot (\sqrt ​ 2 ​ ​ ​)^{​ 2 ​ ​} \cdot \sqrt ​ 2 ​ ​ ​

= 2 \cdot 2 \cdot \sqrt ​ 2 ​ ​ ​ = 4 \sqrt ​ 2 ​ ​ ​

\sqrt ​ 32 ​ ​ ​ = \sqrt ​ 16 ​ ​ ​ \cdot \sqrt ​ 2 ​ ​ ​ = 4 \sqrt ​ 2 ​ ​ ​

Slide 2 - Slide

Calculate the hypotenuse of this triangle. Simplify your answer. (No calculators)

Slide 3 - Open question

5^{​ 2 ​ ​} + (\sqrt ​ 50 ​ ​ ​)^{​ 2 ​ ​} = 25 + 50 = 75

\sqrt ​ 75 ​ ​ ​ = \sqrt ​ 5 ​ ​ ​ \cdot \sqrt ​ 5 ​ ​ ​ \cdot \sqrt ​ 3 ​ ​ ​

= (\sqrt ​ 5 ​ ​ ​)^{​ 2 ​ ​} \cdot \sqrt ​ 3 ​ ​ ​

= 5 \sqrt ​ 3 ​ ​ ​

Slide 4 - Slide

What about this?

Can we simplify it?

\sqrt ​ 3 ​ ​ ​ + \sqrt ​ 2 ​ ​ ​

Slide 5 - Slide

Nope...

Different prime roots must be kept separate, like x's and y's:

<--cannot be simplified

Like roots can be combined:

2 \sqrt ​ 3 ​ ​ ​ + 8 \sqrt ​ 5 ​ ​ ​

3 \sqrt ​ 5 ​ ​ ​ + 4 \sqrt ​ 3 ​ ​ ​ + 2 \sqrt ​ 5 ​ ​ ​ - \sqrt ​ 3 ​ ​ ​

= 5 \sqrt ​ 5 ​ ​ ​ + 3 \sqrt ​ 3 ​ ​ ​

Slide 6 - Slide

Simplify

3 \sqrt ​ 5 ​ ​ ​ + 4 \sqrt ​ 3 ​ ​ ​ + 2 \sqrt ​ 5 ​ ​ ​ - \sqrt ​ 3 ​ ​ ​

2 \sqrt ​ 7 ​ ​ ​ + 4 \sqrt ​ 11 ​ ​ ​ + 2 \sqrt ​ 11 ​ ​ ​ - 3 \sqrt ​ 7 ​ ​ ​

6 \sqrt ​ 11 ​ ​ ​ + 5 \sqrt ​ 7 ​ ​ ​

6 \sqrt ​ 11 ​ ​ ​ - \sqrt ​ 7 ​ ​ ​

\sqrt ​ 11 ​ ​ ​ - 6 \sqrt ​ 7 ​ ​ ​

6 \sqrt ​ 7 ​ ​ ​ - \sqrt ​ 11 ​ ​ ​

Slide 7 - Quiz

(3 x y)^{​ 2 ​ ​} = ?

3 x^{​ 2 ​ ​} y^{​ 2 ​ ​}

3 x y^{​ 2 ​ ​}

9 x^{​ 2 ​ ​} y^{​ 2 ​ ​}

9 x y

Slide 8 - Quiz

Roots work the same way

(4 \sqrt ​ 5 ​ ​ ​)^{​ 2 ​ ​} = 4^{​ 2 ​ ​} \cdot (\sqrt ​ 5 ​ ​ ​)^{​ 2 ​ ​}

= 16 \cdot 5

= 80

(a b c)^{​ 2 ​ ​} = a^{​ 2 ​ ​} b^{​ 2 ​ ​} c^{​ 2 ​ ​}

Slide 9 - Slide

Find the hypotenuse and simplify your answer.

Slide 10 - Open question

(2 \sqrt ​ 3 ​ ​ ​)^{​ 2 ​ ​} + (6 \sqrt ​ 2 ​ ​ ​)^{​ 2 ​ ​}

= 4 \cdot 3 + 36 \cdot 2 = 12 + 72 = 84

\sqrt ​ 84 ​ ​ ​ = \sqrt ​ 2 ​ ​ ​ \cdot \sqrt ​ 2 ​ ​ ​ \cdot \sqrt ​ 3 ​ ​ ​ \cdot \sqrt ​ 7 ​ ​ ​

= 2 \cdot \sqrt ​ 3 ​ ​ ​ \cdot \sqrt ​ 7 ​ ​ ​

= 2 \sqrt ​ 21 ​ ​ ​

Slide 11 - Slide

Slide 12 - Slide

Roots and like terms

Items in this lesson

Slide 1 - Quiz

Slide 2 - Slide

Slide 3 - Open question

Slide 4 - Slide

Slide 5 - Slide

Slide 6 - Slide

Slide 7 - Quiz

Slide 8 - Quiz

Slide 9 - Slide

Slide 10 - Open question

Slide 11 - Slide

Slide 12 - Slide

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