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Multiply Surd Expressions 1

Multiply Surd Expressions 1

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Question 1 of 5

1. Question
Simplify

$\sqrt{5} \times \sqrt{6}$ $sqrt5 xx sqrt6$
- 1. $\sqrt{11}$ $sqrt(11)$
- 2. $\sqrt{65}$ $sqrt(65)$
- 3. $\sqrt{30}$ $sqrt(30)$
- 4. $\sqrt{56}$ $sqrt(56)$
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Multiplication Property of Surds

$\sqrt{a b} = \sqrt{a} \times \sqrt{b}$ $sqrt(ab)=sqrt(a) xx sqrt(b)$

Use the rule above to multiply the surds

$= “ \sqrt{30}$ $=“sqrt(30)$

$\sqrt{5} \times \sqrt{6}$ $sqrt5 xx sqrt6$ $=$ $=$ $\sqrt{5 \times 6}$ $sqrt(5 xx 6)$

$\sqrt{30}$ $sqrt(30)$
Question 2 of 5

2. Question
Simplify

$2 \sqrt{5} \times 2 \sqrt{5}$ $2sqrt5 xx 2sqrt5$
- 1. $\sqrt{20}$ $sqrt(20)$
- 2. $4 \sqrt{10}$ $4sqrt(10)$
- 3. $10$ $10$
- 4. $20$ $20$
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Multiplication Property of Surds

$\sqrt{a b} = \sqrt{a} \times \sqrt{b}$ $sqrt(ab)=sqrt(a) xx sqrt(b)$

Multiply the numbers and then the surds

Multiply numerical coefficients

$2 \times 2$ $2 xx 2$ $=$ $=$ $4$ $4$

Multiply the surds

$\sqrt{5} \times \sqrt{5}$ $sqrt5 xx sqrt5$ $=$ $=$ $\sqrt{25}$ $sqrt(25)$

Combine the products

$=$ $=$ $4$ $4$ $\times$ $xx$ $\sqrt{25}$ $sqrt(25)$ Simplify

$=$ $=$ $4 \times 5$ $4 xx 5$

$=$ $=$ $20$ $20$

$20$ $20$
Question 3 of 5

3. Question
Simplify

$\sqrt{5} \times \sqrt{7}$ $sqrt5 xx sqrt7$
- 1. $\sqrt{12}$ $sqrt(12)$
- 2. $\sqrt{57}$ $sqrt(57)$
- 3. $\sqrt{75}$ $sqrt(75)$
- 4. $\sqrt{35}$ $sqrt(35)$
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Multiplication Property of Surds

$\sqrt{a b} = \sqrt{a} \times \sqrt{b}$ $sqrt(ab)=sqrt(a) xx sqrt(b)$

Use the rule above to multiply the surds

$= “ \sqrt{35}$ $=“sqrt(35)$

$\sqrt{5} \times \sqrt{7}$ $sqrt5 xx sqrt7$ $=$ $=$ $\sqrt{5 \times 7}$ $sqrt(5 xx 7)$

$\sqrt{35}$ $sqrt(35)$
Question 4 of 5

4. Question
Simplify

$\sqrt{3} \times \sqrt{15}$ $sqrt3 xx sqrt15$
- 1. $3 \sqrt{15}$ $3sqrt(15)$
- 2. $5 \sqrt{3}$ $5sqrt(3)$
- 3. $3 \sqrt{5}$ $3sqrt(5)$
- 4. $\sqrt{18}$ $sqrt18$
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Multiplication Property of Surds

$\sqrt{a b} = \sqrt{a} \times \sqrt{b}$ $sqrt(ab)=sqrt(a) xx sqrt(b)$

The radicand of $\sqrt{15}$ $sqrt15$ can be split into its prime factors

$\sqrt{15}$ $sqrt15$ $=$ $=$ $\sqrt{3 \times 5}$ $sqrt(3 xx 5)$

$=$ $=$ $\sqrt{3} \times \sqrt{5}$ $sqrt(3) xx sqrt(5)$

Rewrite the product.

$\sqrt{3} \times \sqrt{15}$ $sqrt(3) xx sqrt15$

$=$ $=$ $\sqrt{3} \times$ $sqrt(3) xx$ $\sqrt{3} \times \sqrt{5}$ $sqrt(3) xx sqrt(5)$ Simplify

$=$ $=$ $3 \sqrt{5}$ $3sqrt(5)$

$3 \sqrt{5}$ $3sqrt(5)$
Question 5 of 5

5. Question
Simplify

$2 \sqrt{5} \times 3 \sqrt{7}$ $2sqrt5 xx 3sqrt7$
- 1. $6 \sqrt{35}$ $6sqrt(35)$
- 2. $5 \sqrt{35}$ $5sqrt(35)$
- 3. $6 \sqrt{12}$ $6sqrt(12)$
- 4. $42 \sqrt{5}$ $42sqrt5$
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Multiplication Property of Surds

$\sqrt{a b} = \sqrt{a} \times \sqrt{b}$ $sqrt(ab)=sqrt(a) xx sqrt(b)$

Multiply the numbers and then the surds

Multiply numerical coefficients

$2 \times 3$ $2 xx 3$ $=$ $=$ $6$ $6$

Multiply the surds

$\sqrt{5} \times \sqrt{7}$ $sqrt5 xx sqrt7$ $=$ $=$ $\sqrt{35}$ $sqrt(35)$

Combine the products

$=$ $=$ $6$ $6$ $\times$ $xx$ $\sqrt{35}$ $sqrt(35)$ Simplify

$=$ $=$ $6 \sqrt{35}$ $6sqrt(35)$

$6 \sqrt{35}$ $6sqrt(35)$

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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