Simplify Surd Expressions using the Distributive Property 2

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Question 1 of 5

Simplify

$sqrt3 (sqrt5 + sqrt7)$

1. $sqrt(15)+sqrt(21)$
2. $sqrt8 +sqrt(10)$
3. $sqrt(15)-sqrt(21)$
4. $6$

Question 2 of 5

Simplify

$sqrt5 (sqrt2 +8)$

1. $8sqrt(10)+sqrt(5)$
2. $sqrt(10)+8sqrt(5)$
3. $8+sqrt(15)$
4. $3sqrt(5)$

Question 3 of 5

Simplify

$sqrt2 (sqrt2 – 4)$

1. $2 - 4sqrt(2)$
2. $1 - 2sqrt(2)$
3. $2 - 2sqrt(4)$
4. $2 + 4sqrt(2)$

Question 4 of 5

Simplify

$3sqrt2 (4sqrt5 + 7)$

1. $12sqrt10 + 21sqrt2$
2. $12sqrt10 - 21sqrt2$
3. $21sqrt10 + 12sqrt2$
4. $21sqrt10 - 12sqrt2$

Question 5 of 5

Simplify

$3sqrt5 (sqrt5 – 2)$

1. $9sqrt5$
2. $6-15sqrt5$
3. $3sqrt25 - 6sqrt5$
4. $15 - 6sqrt(5)$

$color(darkviolet)(sqrt3)(color(royalblue)(sqrt5) + color(forestgreen)(sqrt7))$	$=$	$color(darkviolet)(sqrt3) xx color(royalblue)(sqrt5) + color(darkviolet)(sqrt3) xx color(forestgreen)(sqrt7)$
	$=$	$sqrt(15) + sqrt(21)$	Apply the Multiplication Property

$color(darkviolet)(sqrt5)(color(royalblue)(sqrt2) + color(forestgreen)(8))$	$=$	$color(darkviolet)(sqrt5) xx color(royalblue)(sqrt2) + color(darkviolet)(sqrt5) xx color(forestgreen)(8)$
	$=$	$sqrt(10) + 8sqrt(5)$	Apply the Multiplication Property

$color(darkviolet)(sqrt2)(color(royalblue)(sqrt2) – color(forestgreen)(4))$	$=$	$color(darkviolet)(sqrt2) xx color(royalblue)(sqrt(2)) – color(darkviolet)(sqrt2) xx color(forestgreen)(4)$
	$=$	$2 – 4sqrt(2)$	Apply the Multiplication Property

$color(darkviolet)(3sqrt2)(color(royalblue)(4sqrt5) + color(forestgreen)(7))$	$=$	$color(darkviolet)(3sqrt2) xx color(royalblue)(4sqrt5) + color(darkviolet)(3sqrt2) xx color(forestgreen)(7)$
	$=$	$12sqrt10 + 21sqrt2$	Apply the Multiplication Property

$color(darkviolet)(3sqrt5)(color(royalblue)(sqrt5) -color(forestgreen)(2))$	$=$	$color(darkviolet)(3sqrt5) xx color(royalblue)(sqrt5) – color(darkviolet)(3sqrt5) xx color(forestgreen)(2)$
	$=$	$3sqrt25 – 6sqrt5$	Apply the Multiplication Property
	$=$	$3times5 – 6sqrt5$	25 is a Perfect Square
	$=$	$15 – 6sqrt(5)$	Simplify

Simplify Surd Expressions using the Distributive Property 2

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Quiz summary

Information

1. Question

Hint

Excellent!

Multiplication Property of Surds

Distributive Property

2. Question

Excellent!

Multiplication Property of Surds

Distributive Property

3. Question

Hint

Excellent!

Multiplication Property of Surds

Distributive Property

4. Question

Hint

Excellent!

Multiplication Property of Surds

Distributive Property

5. Question

Hint

Excellent!

Multiplication Property of Surds

Distributive Property

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