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Divide Surd Expressions

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Divide Surd Expressions 2

Divide Surd Expressions 2

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Question 1 of 4

1. Question
Simplify

$\sqrt{48} \div 4$ $sqrt48 -: 4$
- 1. $\sqrt{3}$ $sqrt(3)$
- 2. $4 \sqrt{2}$ $4sqrt(2)$
- 3. $3 \sqrt{2}$ $3sqrt(2)$
- 4. $2 \sqrt{3}$ $2sqrt(3)$
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Division Property of Square Roots

$\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$ $sqrt(a/b)=(sqrt(a))/(sqrt(b))$ or $\sqrt{a \div b} = \sqrt{a} \div \sqrt{b}$ $sqrt(a -: b)=sqrt(a) -: sqrt(b)$

Express both numbers as surds. Get the square of $4$ $4$ and add a surd sign.

$\sqrt{48} \div 4$ $sqrt48 -: 4$ $=$ $=$ $\sqrt{48} \div \sqrt{16}$ $sqrt48 -: sqrt16$ $4^{2} = 16$ $4^2 = 16$

Apply the division property of square roots to simplify the expression

$\sqrt{48} \div \sqrt{16}$ $sqrt48 -: sqrt16$

$=$ $=$ $\sqrt{48 \div 16}$ $sqrt(48 -: 16)$ Divide

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

$\sqrt{3}$ $sqrt(3)$
Question 2 of 4

2. Question
Simplify

$\sqrt{126} \div 3$ $sqrt126 -: 3$
- 1. $\sqrt{42}$ $sqrt(42)$
- 2. $\sqrt{14}$ $sqrt(14)$
- 3. $\sqrt{117}$ $sqrt(117)$
- 4. $3 \sqrt{15}$ $3sqrt(15)$
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Division Property of Square Roots

$\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$ $sqrt(a/b)=(sqrt(a))/(sqrt(b))$ or $\sqrt{a \div b} = \sqrt{a} \div \sqrt{b}$ $sqrt(a -: b)=sqrt(a) -: sqrt(b)$

Express both numbers as surds. Get the square of $3$ $3$ and add a surd sign.

$\sqrt{126} \div 3$ $sqrt126 -: 3$ $=$ $=$ $\sqrt{126} \div \sqrt{9}$ $sqrt126 -: sqrt9$ $3^{2} = 9$ $3^2 = 9$

Apply the division property of square roots to simplify the expression

$\sqrt{126} \div \sqrt{9}$ $sqrt126 -: sqrt9$

$=$ $=$ $\sqrt{126 \div 9}$ $sqrt(126 -: 9)$ Divide

$=$ $=$ $\sqrt{14}$ $sqrt(14)$

$\sqrt{14}$ $sqrt(14)$
Question 3 of 4

3. Question
Simplify

$35 \sqrt{3} \div 5 \sqrt{3}$ $35sqrt3 -: 5sqrt3$
- 1. $175$ $175$
- 2. $7$ $7$
- 3. $7 \sqrt{6}$ $7sqrt(6)$
- 4. $21$ $21$
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Division Property of Square Roots

$\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$ $sqrt(a/b)=(sqrt(a))/(sqrt(b))$ or $\sqrt{a \div b} = \sqrt{a} \div \sqrt{b}$ $sqrt(a -: b)=sqrt(a) -: sqrt(b)$

Apply the division property of square roots to simplify the expression

$35 \sqrt{3} \div 5 \sqrt{3}$ $35sqrt3-: 5sqrt3$

$=$ $=$ $(35 \div 5) \sqrt{3 \div 3}$ $(35-:5)sqrt(3 -: 3)$ Divide

$=$ $=$ $7$ $7$

$7$ $7$
Question 4 of 4

4. Question
Simplify

$12 \sqrt{96} \div 3 \sqrt{2}$ $12sqrt96 -: 3sqrt2$
- 1. $8 \sqrt{6}$ $8sqrt(6)$
- 2. $30 \sqrt{3}$ $30sqrt(3)$
- 3. $4 \sqrt{98}$ $4sqrt(98)$
- 4. $16 \sqrt{3}$ $16sqrt(3)$
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Division Property of Square Roots

$\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$ $sqrt(a/b)=(sqrt(a))/(sqrt(b))$ or $\sqrt{a \div b} = \sqrt{a} \div \sqrt{b}$ $sqrt(a -: b)=sqrt(a) -: sqrt(b)$

Apply the division property of square roots to simplify the expression

$12sqrt96 -: 3sqrt2$

$=$ $(12-:3)sqrt(96 -: 2)$ Divide

$=$ $4sqrt(48)$

$=$ $16sqrt(3)$

$16sqrt(3)$

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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