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Multiply Surd Expressions

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Multiply Surd Expressions 4

Multiply Surd Expressions 4

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Question 1 of 5

1. Question
Simplify

$-3sqrt2 xx 2sqrt5$
- 1. $-6sqrt(7)$
- 2. $-6sqrt(10)$
- 3. $-sqrt(10)$
- 4. $-sqrt7$
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Multiplication Property of Surds

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

Multiply the numbers and then the surds

Multiply numerical coefficients

$-3 xx 2$ $=$ $-6$

Multiply the surds

$sqrt2 xx sqrt5$ $=$ $sqrt(10)$

Combine the products

$=$ $-6$ $xx$ $sqrt(10)$ Simplify

$=$ $-6sqrt(10)$

$-6sqrt(10)$
Question 2 of 5

2. Question
Simplify

$5sqrt27 xx 3sqrt6$
- 1. $135sqrt(2)$
- 2. $30sqrt(9)$
- 3. $81sqrt(2)$
- 4. $15sqrt33$
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Multiplication Property of Surds

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

Multiply the numbers and then the surds

Multiply numerical coefficients

$5 xx 3$ $=$ $15$

Multiply the surds

$sqrt27 xx sqrt6$ $=$ $sqrt(162)$

Combine the products

$=$ $15$ $xx$ $sqrt(162)$ Simplify

$=$ $15 xx sqrt(81) xx sqrt(2)$

$=$ $15 xx 9 xx sqrt(2)$

$=$ $135sqrt(2)$

$135sqrt(2)$
Question 3 of 5

3. Question
Simplify

$-3sqrt7 xx 2sqrt6$
- 1. $-6sqrt(42)$
- 2. $-sqrt(42)$
- 3. $-6sqrt(13)$
- 4. $-sqrt13$
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Multiplication Property of Surds

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

Multiply the numbers and then the surds

Multiply numerical coefficients

$-3 xx 2$ $=$ $-6$

Multiply the surds

$sqrt7 xx sqrt6$ $=$ $sqrt(42)$

Combine the products

$=$ $-6$ $xx$ $sqrt(42)$ Simplify

$=$ $-6sqrt(42)$

$-6sqrt(42)$
Question 4 of 5

4. Question
Simplify

$(4sqrt3)^2$
- 1. $48$
- 2. $12$
- 3. $16sqrt(3)$
- 4. $8sqrt(6)$
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Multiplication Property of Surds

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

Rewrite the square as a multiplication

$(4sqrt3)^2$ $=$ $4sqrt3 xx 4sqrt3$

Multiply the numbers and then the surds

Multiply numerical coefficients

$4 xx 4$ $=$ $16$

Multiply the surds

$sqrt3 xx sqrt3$ $=$ $sqrt(9)$

Combine the products

$=$ $16$ $xx$ $sqrt(9)$ Simplify

$=$ $16 xx 3$

$=$ $48$

$48$
Question 5 of 5

5. Question
Simplify

$6sqrt3 xx 2sqrt6 xx 4sqrt2$
- 1. $288$
- 2. $48sqrt11$
- 3. $72$
- 4. $6sqrt11$
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Multiplication Property of Surds

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

Multiply the numbers and then the surds

Multiply numerical coefficients

$6 xx 2 xx 4$ $=$ $48$

Multiply the surds

$sqrt3 xx sqrt6 xx sqrt2$ $=$ $sqrt(36)$

Combine the products

$=$ $48$ $xx$ $sqrt(36)$ Simplify

$=$ $48 xx 6$

$=$ $288$

$288$

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

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