Simplify Surd Expressions using the Distributive Property 3

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Question 1 of 5

Simplify

$5sqrt6 (3sqrt6 – 3sqrt2)$

1. $90 - 30sqrt(3)$
2. $45 - 15sqrt(3)$
3. $60sqrt(12)$
4. $15 - 15sqrt(3)$

Question 2 of 5

Simplify

$(2sqrt3+3sqrt5) (2sqrt3 + 3sqrt5)$

1. $57 + 12sqrt(15)$
2. $57$
3. $4sqrt6 + 12sqrt15 + 9sqrt10$
4. $57+12sqrt(30)$

Question 3 of 5

Simplify

$4sqrt5 (2sqrt5 – 4sqrt15)$

1. $24sqrt25$
2. $8sqrt(25) - 16sqrt(75)$
3. $8sqrt75$
4. $40 - 80sqrt(3)$

Question 4 of 5

Simplify

$(3sqrt11+4) (3sqrt11 -4)$

1. $83$
2. $9sqrt22 -16$
3. $-15sqrt11 - 16$
4. $9sqrt11 -16$

Question 5 of 5

Simplify

$2sqrt(x) (3sqrt(x) + 2sqrt(y))$

1. $4x + 4sqrt(y)$
2. $4xy + 6sqrt(x)$
3. $24sqrt(xy)$
4. $6x + 4sqrt(xy)$

$color(darkviolet)(5sqrt6)(color(royalblue)(3sqrt6) -color(forestgreen)(3sqrt2))$	$=$	$color(darkviolet)(5sqrt6) xx color(royalblue)(3sqrt6) – color(darkviolet)(5sqrt6) xx color(forestgreen)(3sqrt2)$
	$=$	$15sqrt(36) – 15sqrt(12)$	Apply the Multiplication Property
	$=$	$15 xx 6 – 15 xx 2sqrt(3)$	Simplifying Surds
	$=$	$90 – 30sqrt(3)$	Simplify

$(2sqrt3+3sqrt5) (2sqrt3 + 3sqrt5)$	$=$	$(2sqrt3 xx 2sqrt3) + (2sqrt3 xx 3sqrt5)$
		$+(3sqrt5 xx 2sqrt3) + (3sqrt5 xx 3sqrt5)$
	$=$	$4sqrt9 + 6sqrt(15) + 6sqrt(15) + 9sqrt25$	Apply the Multiplication Property
	$=$	$4 xx 3 + 12sqrt(15) + 9 xx 5$	Simplify
	$=$	$12 + 12sqrt(15) + 45$
	$=$	$57 + 12sqrt(15)$

$color(darkviolet)(4sqrt5)(color(royalblue)(2sqrt5) -color(forestgreen)(4sqrt15))$	$=$	$color(darkviolet)(4sqrt5) xx color(royalblue)(2sqrt5) – color(darkviolet)(4sqrt5) xx color(forestgreen)(4sqrt15)$
	$=$	$8sqrt(25) – 16sqrt(75)$	Apply the Multiplication Property
	$=$	$8 xx 5 – 16 xx 5sqrt(3)$	Simplifying Surds
	$=$	$40 – 80sqrt(3)$	Simplify

$(3sqrt11+4) (3sqrt11 -4)$	$=$	$(3sqrt11 xx 3sqrt11) + (3sqrt11 xx (-4))$
		$+(4 xx 3sqrt11) + (4 xx (-4))$
	$=$	$9sqrt121- 12sqrt(11) + 12sqrt(11) -16$	Apply the Multiplication Property
	$=$	$9 xx 11 -16$	Simplify
	$=$	$99-16$
	$=$	$83$

$color(darkviolet)(2sqrt(x))(color(royalblue)(3sqrt(x)) + color(forestgreen)(2sqrt(y)))$	$=$	$color(darkviolet)(2sqrt(x)) xx color(royalblue)(3sqrt(x)) + color(darkviolet)(2sqrt(x)) xx color(forestgreen)(2sqrt(y))$
	$=$	$6sqrt(x^2) + 4sqrt(xy)$	Apply the Multiplication Property
	$=$	$6x + 4sqrt(xy)$	Simplify

Simplify Surd Expressions using the Distributive Property 3

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Quiz summary

Information

1. Question

Hint

Excellent!

Multiplication Property of Surds

Distributive Property

2. Question

Hint

Keep Going!

Multiplication Property of Surds

Double Bracket Expansion (FOIL) Method

3. Question

Hint

Excellent!

Multiplication Property of Surds

Distributive Property

4. Question

Hint

Fantastic!

Multiplication Property of Surds

Double Bracket Expansion (FOIL) Method

5. Question

Hint

Excellent!

Multiplication Property of Surds

Distributive Property

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