Simplify Square Roots 4 | VividMath

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Year 8

Surds

Simplify Square Roots

Simplify Square Roots 4

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Question 1 of 4

1. Question

Simplify

$\sqrt{18}$ $sqrt18$

1. $6 \sqrt{3}$ $6sqrt(3)$
2. $3 \sqrt{3}$ $3sqrt(3)$
3. $3 \sqrt{5}$ $3sqrt(5)$
4. $3 \sqrt{2}$ $3sqrt(2)$

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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

18 (9)

$18 \ color(forestgreen)((9))$

$\sqrt{18}$ $sqrt(18)$	$=$ $=$	$\sqrt{9 \times 2}$ $sqrt(color(forestgreen)(9) xx 2)$	$9$ $9$ is a perfect square
	$=$ $=$	$\sqrt{9} \times \sqrt{2}$ $sqrt(color(forestgreen)(9)) xx sqrt(2)$	Apply the Multiplication Property
	$=$ $=$	$3 \times \sqrt{2}$ $color(forestgreen)(3) xx sqrt(2)$	$\sqrt{9} = 3$ $color(forestgreen)(sqrt(9)=3)$
	$=$ $=$	$3 \sqrt{2}$ $3sqrt(2)$

3 \sqrt{2}

$3sqrt(2)$

Question 2 of 4

2. Question

Simplify

$2 \sqrt{54}$ $2sqrt54$

1. $6 \sqrt{6}$ $6sqrt(6)$
2. $3 \sqrt{3}$ $3sqrt(3)$
3. $6 \sqrt{5}$ $6sqrt(5)$
4. $5 \sqrt{3}$ $5sqrt(3)$

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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

2 \sqrt{54}

$2sqrt(54)$ , find the largest perfect square that divides evenly into the radicand:

54 (9)

$54 \ color(forestgreen)((9))$

$2 \sqrt{54}$ $2sqrt(54)$	$=$ $=$	$2 \sqrt{9 \times 6}$ $2sqrt(color(forestgreen)(9) xx 6)$	$9$ $9$ is a perfect square
	$=$ $=$	$2 \times \sqrt{9} \times \sqrt{6}$ $2 xx sqrt(color(forestgreen)(9)) xx sqrt(6)$	Apply the Multiplication Property
	$=$ $=$	$2 \times 3 \times \sqrt{6}$ $2 xx color(forestgreen)(3) xx sqrt(6)$	$\sqrt{9} = 3$ $color(forestgreen)(sqrt(9)=3)$
	$=$ $=$	$6 \times \sqrt{6}$ $6 xx sqrt(6)$
	$=$ $=$	$6 \sqrt{6}$ $6sqrt(6)$

6 \sqrt{6}

$6sqrt(6)$

Question 3 of 4

3. Question

Simplify

$3 \sqrt{128}$ $3sqrt128$

1. $24 \sqrt{2}$ $24sqrt(2)$
2. $12 \sqrt{2}$ $12sqrt(2)$
3. $28 \sqrt{3}$ $28sqrt(3)$
4. $7 \sqrt{3}$ $7sqrt(3)$

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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

3 \sqrt{128}

$3sqrt(128)$ , find the largest perfect square that divides evenly into the radicand:

128 (64)

$128 \ color(forestgreen)((64))$

$3 \sqrt{128}$ $3sqrt(128)$	$=$ $=$	$3 \sqrt{64 \times 2}$ $3sqrt(color(forestgreen)(64) xx 2)$	$64$ $64$ is a perfect square
	$=$ $=$	$3 \times \sqrt{64} \times \sqrt{2}$ $3 xx sqrt(color(forestgreen)(64)) xx sqrt(2)$	Apply the Multiplication Property
	$=$ $=$	$3 \times 8 \times \sqrt{2}$ $3 xx color(forestgreen)(8) xx sqrt(2)$	$\sqrt{64} = 8$ $color(forestgreen)(sqrt(64)=8)$
	$=$ $=$	$24 \times \sqrt{2}$ $24 xx sqrt(2)$
	$=$ $=$	$24 \sqrt{2}$ $24sqrt(2)$

24 \sqrt{2}

$24sqrt(2)$

Question 4 of 4

4. Question

Simplify

$2 \sqrt{80}$ $2sqrt80$

1. $4 \sqrt{6}$ $4sqrt(6)$
2. $6 \sqrt{5}$ $6sqrt(5)$
3. $4 \sqrt{5}$ $4sqrt(5)$
4. $8 \sqrt{5}$ $8sqrt(5)$

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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

2 \sqrt{80}

$2sqrt(80)$ , find the largest perfect square that divides evenly into the radicand:

80 (16)

$80 \ color(forestgreen)((16))$

$2 \sqrt{80}$ $2sqrt(80)$	$=$ $=$	$2 \sqrt{16 \times 5}$ $2sqrt(color(forestgreen)(16) xx 5)$	$16$ $16$ is a perfect square
	$=$ $=$	$2 \times \sqrt{16} \times \sqrt{5}$ $2 xx sqrt(color(forestgreen)(16)) xx sqrt(5)$	Apply the Multiplication Property
	$=$ $=$	$2 \times 4 \times \sqrt{5}$ $2 xx color(forestgreen)(4) xx sqrt(5)$	$\sqrt{16} = 4$ $color(forestgreen)(sqrt(16)=4)$
	$=$ $=$	$8 \times \sqrt{5}$ $8 xx sqrt(5)$
	$=$ $=$	$8 \sqrt{5}$ $8sqrt(5)$

8 \sqrt{5}

$8sqrt(5)$

Quizzes

Simplify Square Roots 1
Simplify Square Roots 2
Simplify Square Roots 3
Simplify Square Roots 4
Simplify Surds with Variables 1
Simplify Surds with Variables 2
Simplify Surds with Variables 3
Rewriting Entire and Mixed Surds 1
Rewriting Entire and Mixed Surds 2
Add and Subtract Surd Expressions (Basic) 1
Add and Subtract Surd Expressions (Basic) 2
Add and Subtract Surd Expressions (Basic) 3
Add and Subtract Surd Expressions 1
Add and Subtract Surd Expressions 2
Add and Subtract Surd Expressions 3
Multiply Surd Expressions 1
Multiply Surd Expressions 2
Multiply Surd Expressions 3
Multiply Surd Expressions 4
Divide Surd Expressions 1
Divide Surd Expressions 2
Divide Surd Expressions 3
Multiply and Divide Surd Expressions
Simplify Surd Expressions using the Distributive Property 1
Simplify Surd Expressions using the Distributive Property 2
Simplify Surd Expressions using the Distributive Property 3
Simplify Binomial Surd Expressions using the FOIL Method 1
Simplify Binomial Surd Expressions using the FOIL Method 2
Rationalising the Denominator 1
Rationalising the Denominator 2
Rationalising the Denominator 3
Rationalising the Denominator 4
Rationalising the Denominator using Conjugates