Simplify Radical Expressions using the Distributive Property 2

Question 1 of 5

Simplify

$\sqrt{3} (\sqrt{5} + \sqrt{7})$ $sqrt3 (sqrt5 + sqrt7)$

1. $\sqrt{15} + \sqrt{21}$ $sqrt(15)+sqrt(21)$
2. $\sqrt{8} + \sqrt{10}$ $sqrt8 +sqrt(10)$
3. $6$ $6$
4. $\sqrt{15} - \sqrt{21}$ $sqrt(15)-sqrt(21)$

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Multiplication Property of Radicals

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

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

Distributive Property

a (b + c) = a b + a c

$color(darkviolet)(a)(color(royalblue)(b)+color(forestgreen)(c))=color(darkviolet)(a)color(royalblue)(b)+color(darkviolet)(a)color(forestgreen)(c)$

Apply the Distributive Property.

$\sqrt{3} (\sqrt{5} + \sqrt{7})$ $color(darkviolet)(sqrt3)(color(royalblue)(sqrt5) + color(forestgreen)(sqrt7))$	$=$ $=$	$\sqrt{3} \times \sqrt{5} + \sqrt{3} \times \sqrt{7}$ $color(darkviolet)(sqrt3) xx color(royalblue)(sqrt5) + color(darkviolet)(sqrt3) xx color(forestgreen)(sqrt7)$
	$=$ $=$	$\sqrt{15} + \sqrt{21}$ $sqrt(15) + sqrt(21)$	Apply the Multiplication Property

\sqrt{15} + \sqrt{21}

$sqrt(15)+sqrt(21)$

Question 2 of 5

Simplify

$\sqrt{5} (\sqrt{2} + 8)$ $sqrt5 (sqrt2 +8)$

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

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Multiplication Property of Radicals

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

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

Distributive Property

a (b + c) = a b + a c

$color(darkviolet)(a)(color(royalblue)(b)+color(forestgreen)(c))=color(darkviolet)(a)color(royalblue)(b)+color(darkviolet)(a)color(forestgreen)(c)$

Apply the Distributive Property.

$\sqrt{5} (\sqrt{2} + 8)$ $color(darkviolet)(sqrt5)(color(royalblue)(sqrt2) + color(forestgreen)(8))$	$=$ $=$	$\sqrt{5} \times \sqrt{2} + \sqrt{5} \times 8$ $color(darkviolet)(sqrt5) xx color(royalblue)(sqrt2) + color(darkviolet)(sqrt5) xx color(forestgreen)(8)$
	$=$ $=$	$\sqrt{10} + 8 \sqrt{5}$ $sqrt(10) + 8sqrt(5)$	Apply the Multiplication Property

\sqrt{10} + 8 \sqrt{5}

$sqrt(10)+8sqrt(5)$

Question 3 of 5

Simplify

$\sqrt{2} (\sqrt{2} - 4)$ $sqrt2 (sqrt2 – 4)$

1. $1 - 2 \sqrt{2}$ $1 - 2sqrt(2)$
2. $2 + 4 \sqrt{2}$ $2 + 4sqrt(2)$
3. $2 - 2 \sqrt{4}$ $2 - 2sqrt(4)$
4. $2 - 4 \sqrt{2}$ $2 - 4sqrt(2)$

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Multiplication Property of Radicals

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

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

Distributive Property

a (b + c) = a b + a c

$color(darkviolet)(a)(color(royalblue)(b)+color(forestgreen)(c))=color(darkviolet)(a)color(royalblue)(b)+color(darkviolet)(a)color(forestgreen)(c)$

Apply the Distributive Property.

$\sqrt{2} (\sqrt{2} - 4)$ $color(darkviolet)(sqrt2)(color(royalblue)(sqrt2) – color(forestgreen)(4))$	$=$ $=$	$\sqrt{2} \times \sqrt{2} - \sqrt{2} \times 4$ $color(darkviolet)(sqrt2) xx color(royalblue)(sqrt(2)) – color(darkviolet)(sqrt2) xx color(forestgreen)(4)$
	$=$ $=$	$2 - 4 \sqrt{2}$ $2 – 4sqrt(2)$	Apply the Multiplication Property

2 - 4 \sqrt{2}

$2 – 4sqrt(2)$

Question 4 of 5

Simplify

$3 \sqrt{2} (4 \sqrt{5} + 7)$ $3sqrt2 (4sqrt5 + 7)$

1. $12 \sqrt{10} + 21 \sqrt{2}$ $12sqrt10 + 21sqrt2$
2. $21 \sqrt{10} - 12 \sqrt{2}$ $21sqrt10 - 12sqrt2$
3. $12 \sqrt{10} - 21 \sqrt{2}$ $12sqrt10 - 21sqrt2$
4. $21 \sqrt{10} + 12 \sqrt{2}$ $21sqrt10 + 12sqrt2$

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Multiplication Property of Radicals

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

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

Distributive Property

a (b + c) = a b + a c

$color(darkviolet)(a)(color(royalblue)(b)+color(forestgreen)(c))=color(darkviolet)(a)color(royalblue)(b)+color(darkviolet)(a)color(forestgreen)(c)$

Apply the Distributive Property.

$3 \sqrt{2} (4 \sqrt{5} + 7)$ $color(darkviolet)(3sqrt2)(color(royalblue)(4sqrt5) + color(forestgreen)(7))$	$=$ $=$	$3 \sqrt{2} \times 4 \sqrt{5} + 3 \sqrt{2} \times 7$ $color(darkviolet)(3sqrt2) xx color(royalblue)(4sqrt5) + color(darkviolet)(3sqrt2) xx color(forestgreen)(7)$
	$=$ $=$	$12 \sqrt{10} + 21 \sqrt{2}$ $12sqrt10 + 21sqrt2$	Apply the Multiplication Property

12 \sqrt{10} + 21 \sqrt{2}

$12sqrt10 + 21sqrt2$

Question 5 of 5

Simplify

$3 \sqrt{5} (\sqrt{5} - 2)$ $3sqrt5 (sqrt5 – 2)$

1. $15 - 6 \sqrt{5}$ $15 - 6sqrt(5)$
2. $3 \sqrt{25} - 6 \sqrt{5}$ $3sqrt25 - 6sqrt5$
3. $6 - 15 \sqrt{5}$ $6-15sqrt5$
4. $9 \sqrt{5}$ $9sqrt5$

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Multiplication Property of Radicals

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

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

Distributive Property

a (b + c) = a b + a c

$color(darkviolet)(a)(color(royalblue)(b)+color(forestgreen)(c))=color(darkviolet)(a)color(royalblue)(b)+color(darkviolet)(a)color(forestgreen)(c)$

Apply the Distributive Property.

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

15 - 6 \sqrt{5}

$15 – 6sqrt(5)$

Simplify Radical Expressions using the Distributive Property 2

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Quiz summary

Information

1. Question

Hint

Excellent!

Multiplication Property of Radicals

Distributive Property

2. Question

Excellent!

Multiplication Property of Radicals

Distributive Property

3. Question

Hint

Excellent!

Multiplication Property of Radicals

Distributive Property

4. Question

Hint

Excellent!

Multiplication Property of Radicals

Distributive Property

5. Question

Hint

Excellent!

Multiplication Property of Radicals

Distributive Property

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