Simplify Square Roots 2 | VividMath

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Year 8

Surds

Simplify Square Roots

Simplify Square Roots 2

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Question 1 of 5

1. Question

Simplify

$\sqrt{45}$ $sqrt45$

1. $9 \sqrt{3}$ $9sqrt(3)$
2. $3 \sqrt{3}$ $3sqrt(3)$
3. $9 \sqrt{5}$ $9sqrt(5)$
4. $3 \sqrt{5}$ $3sqrt(5)$

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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

45 (9)

$45 \ color(forestgreen)((9))$

$\sqrt{45}$ $sqrt(45)$	$=$ $=$	$\sqrt{9 \times 5}$ $sqrt(color(forestgreen)(9) xx 5)$	$9$ $color(forestgreen)(9)$ is a perfect square
	$=$ $=$	$\sqrt{9} \times \sqrt{5}$ $color(forestgreen)(sqrt9) xx sqrt5$	Apply the Multiplication Property
	$=$ $=$	$3 \times \sqrt{5}$ $color(forestgreen)(3) xx sqrt(5)$	$\sqrt{9} = 3$ $color(forestgreen)(sqrt9=3)$
	$=$ $=$	$3 \sqrt{5}$ $3sqrt(5)$

3 \sqrt{5}

$3sqrt(5)$

Question 2 of 5

2. Question

Simplify

$\sqrt{48}$ $sqrt48$

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

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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

48 (4)

$48 \ color(forestgreen)((4))$

$\sqrt{48}$ $sqrt(48)$	$=$ $=$	$\sqrt{4 \times 12}$ $sqrt(color(forestgreen)(4) xx 12)$	$4$ $4$ is a perfect square
	$=$ $=$	$\sqrt{4} \times \sqrt{12}$ $sqrt(color(forestgreen)(4)) xx sqrt(12)$	Apply the Multiplication Property
	$=$ $=$	$2 \times \sqrt{12}$ $color(forestgreen)(2) xx sqrt(12)$	$\sqrt{4} = 2$ $color(forestgreen)(sqrt(4)=2)$
	$=$ $=$	$2 \times \sqrt{4 \times 3}$ $2 xx sqrt(4 xx 3)$	Factor again by finding smaller multiples of $12$ $12$
	$=$ $=$	$2 \times \sqrt{4} \times \sqrt{3}$ $2 xx sqrt(4) xx sqrt(3)$	Apply the Multiplication Property
	$=$ $=$	$2 \times 2 \times \sqrt{3}$ $2 xx 2 xx sqrt(3)$	$4$ $4$ is a perfect square
	$=$ $=$	$4 \times \sqrt{3}$ $4 xx sqrt(3)$
	$=$ $=$	$4 \sqrt{3}$ $4sqrt(3)$

4 \sqrt{3}

$4sqrt(3)$

Question 3 of 5

3. Question

Simplify

$\sqrt{125}$ $sqrt125$

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

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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

125 (25)

$125 \ color(forestgreen)((25))$

$\sqrt{125}$ $sqrt(125)$	$=$ $=$	$\sqrt{25 \times 5}$ $sqrt(color(forestgreen)(25) xx 5)$	$25$ $25$ is a perfect square
	$=$ $=$	$\sqrt{25} \times \sqrt{5}$ $sqrt(color(forestgreen)(25)) xx sqrt(5)$	Apply the Multiplication Property
	$=$ $=$	$5 \times \sqrt{5}$ $color(forestgreen)(5) xx sqrt(5)$	$\sqrt{25} = 5$ $color(forestgreen)(sqrt(25)=5)$
	$=$ $=$	$5 \sqrt{5}$ $5sqrt(5)$

5 \sqrt{5}

$5sqrt(5)$

Question 4 of 5

4. Question

Simplify

$\sqrt{98}$ $sqrt98$

1. $7 \sqrt{2}$ $7sqrt(2)$
2. $5 \sqrt{2}$ $5sqrt(2)$
3. $9 \sqrt{7}$ $9sqrt(7)$
4. $9 \sqrt{2}$ $9sqrt(2)$

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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

98 (49)

$98 \ color(forestgreen)((49))$

$\sqrt{98}$ $sqrt(98)$	$=$ $=$	$\sqrt{49 \times 2}$ $sqrt(color(forestgreen)(49) xx 2)$	$49$ $49$ is a perfect square
	$=$ $=$	$\sqrt{49} \times \sqrt{2}$ $sqrt(color(forestgreen)(49)) xx sqrt(2)$	Apply the Multiplication Property
	$=$ $=$	$7 \times \sqrt{2}$ $color(forestgreen)(7) xx sqrt(2)$	$\sqrt{49} = 7$ $color(forestgreen)(sqrt(49)=7)$
	$=$ $=$	$7 \sqrt{2}$ $7sqrt(2)$

7 \sqrt{2}

$7sqrt(2)$

Question 5 of 5

5. Question

Simplify

$\sqrt{72}$ $sqrt72$

1. $6 \sqrt{2}$ $6sqrt(2)$
2. $5 \sqrt{2}$ $5sqrt(2)$
3. $2 \sqrt{3}$ $2sqrt(3)$
4. $7 \sqrt{2}$ $7sqrt(2)$

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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

72 (36)

$72 \ color(forestgreen)((36))$

$\sqrt{72}$ $sqrt(72)$	$=$ $=$	$\sqrt{36 \times 2}$ $sqrt(color(forestgreen)(36) xx 2)$	$36$ $36$ is a perfect square
	$=$ $=$	$\sqrt{36} \times \sqrt{2}$ $sqrt(color(forestgreen)(36)) xx sqrt(2)$	Apply the Multiplication Property
	$=$ $=$	$6 \times \sqrt{2}$ $color(forestgreen)(6) xx sqrt(2)$	$\sqrt{36} = 6$ $color(forestgreen)(sqrt(36)=6)$
	$=$ $=$	$6 \sqrt{2}$ $6sqrt(2)$

6 \sqrt{2}

$6sqrt(2)$

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