Simplify Square Roots 3

Question 1 of 5

Simplify.

\sqrt{108}

$sqrt(108)$

1. $3 \sqrt{36}$ $3sqrt36$
2. $36 \sqrt{3}$ $36sqrt3$
3. $3 \sqrt{6}$ $3sqrt6$
4. $6 \sqrt{3}$ $6sqrt3$

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Multiplication Property of Surds

\sqrt{a b} = \sqrt{a} \times \sqrt{b}

$sqrt(ab)=sqrt(a) xx sqrt(b)$

To simplify

\sqrt{108}

$sqrt(108)$ , find factors that are perfect squares

$\sqrt{108}$ $sqrt(108)$	$=$ $=$	$\sqrt{36 \times 3}$ $sqrt(36 xx 3)$	Factor by finding smaller multiples of $108$ $108$
	$=$ $=$	$\sqrt{36} \times \sqrt{3}$ $sqrt(36) xx sqrt(3)$	Apply the Surd Multiplication Property
	$=$ $=$	$6 \times \sqrt{3}$ $6 xx sqrt(3)$	$36$ $36$ is a perfect square
	$=$ $=$	$6 \sqrt{3}$ $6sqrt(3)$

6 \sqrt{3}

$6sqrt(3)$

Question 2 of 5

Simplify

\sqrt{432}

$sqrt432$

1. $13 \sqrt{2}$ $13sqrt2$
2. $12 \sqrt{3}$ $12sqrt3$
3. $6 \sqrt{2}$ $6sqrt2$
4. $8 \sqrt{3}$ $8sqrt3$

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Multiplication Property of Surds

\sqrt{a b} = \sqrt{a} \times \sqrt{b}

$sqrt(ab)=sqrt(a) xx sqrt(b)$

To simplify

\sqrt{432}

$sqrt(432)$ , find factors that are perfect squares

$\sqrt{432}$ $sqrt(432)$	$=$ $=$	$\sqrt{144 \times 3}$ $sqrt(144 xx 3)$	Factor by finding smaller multiples of $432$ $432$
	$=$ $=$	$\sqrt{144} \times \sqrt{3}$ $sqrt(144) xx sqrt(3)$	Apply the Surd Multiplication Property
	$=$ $=$	$12 \times \sqrt{3}$ $12 xx sqrt(3)$	$144$ $144$ is a perfect square
	$=$ $=$	$12 \sqrt{3}$ $12sqrt(3)$

12 \sqrt{3}

$12sqrt(3)$

Question 3 of 5

Simplify

3 \sqrt{200}

$3sqrt200$

1. $30 \sqrt{2}$ $30sqrt2$
2. $10 \sqrt{2}$ $10sqrt2$
3. $10 \sqrt{3}$ $10sqrt3$
4. $10 \sqrt{6}$ $10sqrt6$

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Multiplication Property of Surds

\sqrt{a b} = \sqrt{a} \times \sqrt{b}

$sqrt(ab)=sqrt(a) xx sqrt(b)$

First, you can separate the coefficient from the square root.

3 \sqrt{200}

$3sqrt(200)$

=

$=$

3 \times \sqrt{200}

$3 xx sqrt(200)$

Next, to simplify

\sqrt{200}

$sqrt(200)$ , find factors that are perfect squares

$3 \times \sqrt{200}$ $3 xx sqrt(200)$	$=$ $=$	$3 \times \sqrt{100 \times 2}$ $3 xx sqrt(100xx2)$	Factor by finding smaller multiples of $432$ $432$
	$=$ $=$	$3 \times \sqrt{100} \times \sqrt{2}$ $3 xx sqrt(100) xx sqrt(2)$	Apply the Surd Multiplication Property
	$=$ $=$	$3 \times 10 \times \sqrt{2}$ $3 xx 10 xx sqrt(2)$	$100$ $100$ is a perfect square
	$=$ $=$	$30 \times \sqrt{2}$ $30 xx sqrt(2)$
	$=$ $=$	$30 \sqrt{2}$ $30sqrt(2)$

30 \sqrt{2}

$30sqrt(2)$

Question 4 of 5

Simplify

8 \sqrt{48}

$8sqrt48$

1. $32 \sqrt{3}$ $32sqrt3$
2. $16 \sqrt{12}$ $16sqrt12$
3. $16 \sqrt{3}$ $16sqrt3$
4. $4 \sqrt{12}$ $4sqrt12$

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Multiplication Property of Surds

\sqrt{a b} = \sqrt{a} \times \sqrt{b}

$sqrt(ab)=sqrt(a) xx sqrt(b)$

First, you can separate the coefficient from the square root.

8 \sqrt{48}

$8sqrt(48)$

=

$=$

8 \times \sqrt{48}

$8 xx sqrt(48)$

Next, to simplify

\sqrt{48}

$sqrt(48)$ , find factors that are perfect squares

$8 \times \sqrt{48}$ $8 xx sqrt(48)$	$=$ $=$	$8 \times \sqrt{16 \times 3}$ $8 xx sqrt(16xx3)$	Factor by finding smaller multiples of $48$ $48$
	$=$ $=$	$8 \times \sqrt{16} \times \sqrt{3}$ $8 xx sqrt(16) xx sqrt(3)$	Apply the Surd Multiplication Property
	$=$ $=$	$8 \times 4 \times \sqrt{3}$ $8 xx 4 xx sqrt(3)$	$16$ $16$ is a perfect square
	$=$ $=$	$32 \times \sqrt{3}$ $32 xx sqrt(3)$
	$=$ $=$	$32 \sqrt{3}$ $32sqrt(3)$

Alternatively, you can use other square factors of

48

$48$ and get the same simplified value. Take note that the process will be longer if you are not using the highest square factor.

$8 \times \sqrt{48}$ $8 xx sqrt(48)$	$=$ $=$	$8 \times \sqrt{4 \times 12}$ $8 xx sqrt(4xx12)$	$4$ $4$ and $12$ $12$ are factors of $48$ $48$
	$=$ $=$	$8 \times \sqrt{4} \times \sqrt{12}$ $8 xx sqrt(4) xx sqrt(12)$	Apply the Surd Multiplication Property
	$=$ $=$	$8 \times 2 \times \sqrt{12}$ $8 xx 2 xx sqrt(12)$	$4$ $4$ is a perfect square
	$=$ $=$	$16 \times \sqrt{4 \times 3}$ $16 xx sqrt(4xx3)$	$4$ $4$ and $3$ $3$ are factors of $12$ $12$
	$=$ $=$	$16 \times \sqrt{4} \times \sqrt{3}$ $16 xx sqrt(4) xx sqrt(3)$	Apply the Surd Multiplication Property
	$=$ $=$	$16 \times 2 \times \sqrt{3}$ $16 xx 2 xx sqrt(3)$	$4$ $4$ is a perfect square
	$=$ $=$	$32 \times \sqrt{3}$ $32 xx sqrt(3)$
	$=$ $=$	$32 \sqrt{3}$ $32sqrt(3)$

32 \sqrt{3}

$32sqrt(3)$

Question 5 of 5

Simplify

$\sqrt{63}$ $sqrt63$

1. $3 \sqrt{7}$ $3sqrt(7)$
2. $9 \sqrt{7}$ $9sqrt(7)$
3. $3 \sqrt{3}$ $3sqrt(3)$
4. $9 \sqrt{3}$ $9sqrt(3)$

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Multiplication Property of Surds

\sqrt{a b} = \sqrt{a} \times \sqrt{b}

$sqrt(ab)=sqrt(a) xx sqrt(b)$

First, find the largest perfect square that divides evenly into

63 (9)

$63 \ color(forestgreen)((9))$

$\sqrt{63}$ $sqrt(63)$	$=$ $=$	$\sqrt{9 \times 7}$ $sqrt(color(forestgreen)(9) xx 7)$	$9$ $9$ is a perfect square
	$=$ $=$	$\sqrt{9} \times \sqrt{7}$ $sqrt(color(forestgreen)(9)) xx sqrt(7)$	Apply the Multiplication Property
	$=$ $=$	$9 \times \sqrt{7}$ $color(forestgreen)(9) xx sqrt(7)$	$\sqrt{9} = 3$ $color(forestgreen)(sqrt(9)=3)$
	$=$ $=$	$3 \sqrt{7}$ $3sqrt(7)$

3 \sqrt{7}

$3sqrt(7)$

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Quiz summary

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1. Question

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Fantastic!

Multiplication Property of Surds

2. Question

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Nice Job!

Multiplication Property of Surds

3. Question

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Great Work!

Multiplication Property of Surds

4. Question

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Correct!

Multiplication Property of Surds

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Excellent!

Multiplication Property of Surds

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