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Multiply Surd Expressions

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Multiply Surd Expressions 1

Multiply Surd Expressions 1

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Question 1 of 5

1. Question
Simplify

$sqrt5 xx sqrt6$
- 1. $sqrt(65)$
- 2. $sqrt(56)$
- 3. $sqrt(11)$
- 4. $sqrt(30)$
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Multiplication Property of Surds

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

Use the rule above to multiply the surds

$=“sqrt(30)$

$sqrt5 xx sqrt6$ $=$ $sqrt(5 xx 6)$

$sqrt(30)$
Question 2 of 5

2. Question
Simplify

$2sqrt5 xx 2sqrt5$
- 1. $20$
- 2. $10$
- 3. $sqrt(20)$
- 4. $4sqrt(10)$
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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

$2 xx 2$ $=$ $4$

Multiply the surds

$sqrt5 xx sqrt5$ $=$ $sqrt(25)$

Combine the products

$=$ $4$ $xx$ $sqrt(25)$ Simplify

$=$ $4 xx 5$

$=$ $20$

$20$
Question 3 of 5

3. Question
Simplify

$sqrt5 xx sqrt7$
- 1. $sqrt(35)$
- 2. $sqrt(12)$
- 3. $sqrt(57)$
- 4. $sqrt(75)$
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Multiplication Property of Surds

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

Use the rule above to multiply the surds

$=“sqrt(35)$

$sqrt5 xx sqrt7$ $=$ $sqrt(5 xx 7)$

$sqrt(35)$
Question 4 of 5

4. Question
Simplify

$sqrt3 xx sqrt15$
- 1. $3sqrt(15)$
- 2. $5sqrt(3)$
- 3. $sqrt18$
- 4. $3sqrt(5)$
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Multiplication Property of Surds

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

The radicand of $sqrt15$ can be split into its prime factors

$sqrt15$ $=$ $sqrt(3 xx 5)$

$=$ $sqrt(3) xx sqrt(5)$

Rewrite the product.

$sqrt(3) xx sqrt15$

$=$ $sqrt(3) xx$ $sqrt(3) xx sqrt(5)$ Simplify

$=$ $3sqrt(5)$

$3sqrt(5)$
Question 5 of 5

5. Question
Simplify

$2sqrt5 xx 3sqrt7$
- 1. $6sqrt(12)$
- 2. $5sqrt(35)$
- 3. $6sqrt(35)$
- 4. $42sqrt5$
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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

$2 xx 3$ $=$ $6$

Multiply the surds

$sqrt5 xx sqrt7$ $=$ $sqrt(35)$

Combine the products

$=$ $6$ $xx$ $sqrt(35)$ Simplify

$=$ $6sqrt(35)$

$6sqrt(35)$

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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