Multiply Surd Expressions 3 | VividMath

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Year 8

Surds

Multiply Surd Expressions

Multiply Surd Expressions 3

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Question 1 of 5

1. Question

Simplify

$4sqrt18 xx 6sqrt5$

1. $24sqrt(8)$
2. $72sqrt(10)$
3. $36sqrt(6)$
4. $20sqrt(14)$

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Multiplication Property of Square Roots

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

Multiply the coefficients and then the radicands of each term

$color(royalblue)(4)color(forestgreen)(sqrt18) xx color(royalblue)(6)color(forestgreen)(sqrt5)$

Multiply numerical coefficients

$color(royalblue)(4 xx 6)$

$=$

$24$

Multiply the radicands

$color(forestgreen)(sqrt18 xx sqrt5)$

$=$

$sqrt(90)$

Combine the products

$=$	$24 xx sqrt(90)$	Factor by finding smaller multiples of $48$
$=$	$24 xx sqrt(9) xx sqrt(10)$	Apply the Multiplication Property
$=$	$24 xx 3 xx sqrt(10)$	$9$ is a perfect square
$=$	$72sqrt(10)$

$72sqrt(10)$

Question 2 of 5

2. Question

Simplify

$7sqrt6 xx 2sqrt8$

1. $56sqrt(8)$
2. $28sqrt(10)$
3. $42sqrt(6)$
4. $56sqrt(3)$

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Multiplication Property of Square Roots

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

Multiply the coefficients and then the radicands of each term

$color(royalblue)(7)color(forestgreen)(sqrt6) xx color(royalblue)(2)color(forestgreen)(sqrt8)$

Multiply numerical coefficients

$color(royalblue)(7 xx 2)$

$=$

$14$

Multiply the radicands

$color(forestgreen)(sqrt6 xx sqrt8)$

$=$

$sqrt(48)$

Combine the products

$=$	$14 xx sqrt(48)$	Factor by finding smaller multiples of $48$
$=$	$14 xx sqrt(16) xx sqrt(3)$	Apply the Multiplication Property
$=$	$14 xx 4 xx sqrt(3)$	$16$ is a perfect square
$=$	$56sqrt(3)$

$56sqrt(3)$

Question 3 of 5

3. Question

Simplify

$2sqrt6 xx 6sqrt3$

1. $4sqrt(11)$
2. $18sqrt(6)$
3. $36sqrt(2)$
4. $16sqrt(22)$

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Multiplication Property of Square Roots

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

Multiply the coefficients and then the radicands of each term

$color(royalblue)(2)color(forestgreen)(sqrt6) xx color(royalblue)(6)color(forestgreen)(sqrt3)$

Multiply numerical coefficients

$color(royalblue)(2 xx 6)$

$=$

$12$

Multiply the radicands

$color(forestgreen)(sqrt6 xx sqrt3)$

$=$

$sqrt(18)$

Combine the products

$=$	$12 xx sqrt(18)$	Factor by finding smaller multiples of $18$
$=$	$12 xx sqrt(9) xx sqrt(2)$	Apply the Multiplication Property
$=$	$12 xx 3 xx sqrt(2)$	$36$ is a perfect square
$=$	$36sqrt(2)$

$36sqrt(2)$

Question 4 of 5

4. Question

Simplify

$4sqrt3 xx 2sqrt3 xx sqrt2$

1. $24sqrt(2)$
2. $18sqrt(3)$
3. $21sqrt6$
4. $20sqrt(5)$

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Multiplication Property of Square Roots

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

Multiply the coefficients and then the radicands of each term. Remember that if there’s no radicand, the radicand is

$1$ .

$color(royalblue)(4)color(forestgreen)(sqrt3) xx color(royalblue)(2)color(forestgreen)(sqrt3) xx color(royalblue)(1)color(forestgreen)(sqrt2)$

Multiply numerical coefficients

$color(royalblue)(4 xx 2 xx 1)$

$=$

$8$

Multiply the radicands

$color(forestgreen)(sqrt3 xx sqrt3 xx sqrt2)$

$=$

$sqrt(18)$

Combine the products

$=$	$8 xx sqrt(18)$	Factor by finding smaller multiples of $18$
$=$	$8 xx sqrt(9) xx sqrt(2)$	Apply the Multiplication Property
$=$	$8 xx 3 xx sqrt(2)$	$9$ is a perfect square
$=$	$24sqrt(2)$

$24sqrt(2)$

Question 5 of 5

5. Question

Simplify

$5sqrt6 xx 2sqrt5 xx 3sqrt2$

1. $45sqrt(8)$
2. $30sqrt(21)$
3. $60sqrt(15)$
4. $15sqrt(10)$

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Multiplication Property of Square Roots

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

Multiply the coefficients and then the radicands of each term

$color(royalblue)(5)color(forestgreen)(sqrt6) xx color(royalblue)(2)color(forestgreen)(sqrt5) xx color(royalblue)(3)color(forestgreen)(sqrt2)$

Multiply numerical coefficients

$color(royalblue)(5 xx 2 xx 3)$

$=$

$30$

Multiply the radicands

$color(forestgreen)(sqrt6 xx sqrt5 xx sqrt2)$

$=$

$sqrt(60)$

Combine the products

$=$	$30 xx sqrt(60)$	Factor by finding smaller multiples of $60$
$=$	$30 xx sqrt(4) xx sqrt(15)$	Apply the Multiplication Property
$=$	$30 xx 2 xx sqrt(15)$	$4$ is a perfect square
$=$	$60sqrt(15)$

$60sqrt(15)$

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