Simplify Surds with Variables 1
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Question 1 of 5
1. Question
Simplify`8sqrt(162a)`Hint
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Multiplication Property of Surds
`sqrt(ab)=sqrt(a) xx sqrt(b)`Find factors that are perfect squares for `sqrt(162a)``8 sqrt(162a)` `=` `8 sqrt(81 xx 2 xx a)` Factor by finding the greatest perfect square of `162` `=` `8 xx sqrt81 xx sqrt2 xx sqrta` Apply the Multiplication Property `=` `8 xx 9 xx sqrt2 xx sqrta` `81` is a perfect square `=` `72 xx sqrt2 xx sqrta` `=` `72 sqrt(2a)` `72 sqrt(2a)` -
Question 2 of 5
2. Question
Simplify`sqrt(24x^2)`Hint
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Multiplication Property of Surds
`sqrt(ab)=sqrt(a) xx sqrt(b)`First, separate the variable from the constant.`sqrt(24x^2)` `=` `sqrt(24)`` xx ``sqrt(x^2)` Apply the Multiplication Property Next, simplify the variable by rewriting the square root in `sqrt(x^2)` as a fractional exponent`sqrt(x^2)` `=` `(x^2)^(1/2)` `=` `x` Use the Power Rule to simplify `(x^a)^(b)=x^(ab)` Finally, find factors that are perfect squares for `sqrt24 xx x`$$\color{#007DDC}{\sqrt{24}}\times\color{#9a00c7}{x}$$ `=` `sqrt(4 xx 6)`` xx ``x` `=` `sqrt4 xx sqrt6 xx x` Apply the Multiplication Property `=` `2 xx sqrt6 xx x` `4` is a perfect square `=` `2xsqrt6` Rearrange the expression `2xsqrt6` -
Question 3 of 5
3. Question
Simplify`sqrt(16x^3)`Hint
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Multiplication Property of Surds
`sqrt(ab)=sqrt(a) xx sqrt(b)`First, separate the variable from the constant.`sqrt(16x^3)` `=` `sqrt(16)`` xx ``sqrt(x^3)` Apply the Multiplication Property Next, simplify the variable by rewriting the square root in `sqrt(x^3)` as a fractional exponent`sqrt(x^3)` `=` `sqrt(x^2 xx x)` `sqrt(x^3)` `=` `sqrt(x^2) xx sqrtx` Apply the Multiplication Property `=` `x xx sqrtx` Use the Power Rule to simplify `(x^a)^(b)=x^(ab)` `=` `xsqrtx` Finally, find factors that are perfect squares for `sqrt16 xx xsqrtx`$$\color{#007DDC}{\sqrt{16}}\times\color{#9a00c7}{x\sqrt{x}}$$ `=` `4`` xx ``x` `=` `4xsqrtx` Rearrange the expression `4xsqrtx` -
Question 4 of 5
4. Question
Simplify`sqrt(9(y+7)^4)`Hint
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Multiplication Property of Surds
`sqrt(ab)=sqrt(a) xx sqrt(b)`First, separate the variable from the constant.`sqrt(9(y+7)^4)` `=` `sqrt(9)`` xx ``sqrt((y+7)^4)` Apply the Multiplication Property Next, get the factor of `sqrt((y+7)^4)` and simplify`sqrt((y+7)^4)` `=` `sqrt((y+7)^2 xx (y+7)^2)` `=` `(y+7)^2` `(y+7)^4` is a perfect square Finally, find factors that are perfect squares for `sqrt9 xx (y+7)^2`$$\color{#007DDC}{\sqrt{9}}\times\color{#9a00c7}{(y+7)^2}$$ `=` `3`` xx ``(y+7)^2` `=` `3(y+7)^2` `3(y+7)^2` -
Question 5 of 5
5. Question
Simplify`sqrt(x^7)`Hint
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Multiplication Property of Surds
`sqrt(ab)=sqrt(a) xx sqrt(b)`Find factors that are perfect squares for `sqrt(x^7)``sqrt(x^7)` `=` `sqrt(x^6) xx sqrtx` Find the highest even factor of `x^7` `=` `x^3 xx sqrtx` `sqrt(x^6)` is a perfect square `=` `x^3sqrtx` `x^3sqrtx`
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