Simplify Surds with Variables 2

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Question 1 of 4

1. Question
Simplify

`5sqrt(a^8)`
- `5a^4`
- `5 sqrt(a^2)`
- `20`
- `5a^2`
Hint

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Correct

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Incorrect

Multiplication Property of Surds

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

Rewrite the square root as an exponent

`sqrt(a^8)` `=` `(a^8)^(1/2)` `x^(1/2)` is the same as `sqrtx`

`=` `a^4` Use the Power Rule to simplify `(x^a)^b = x^(ab)`

Simplify

`=` `5xx``a^4`

`=` `5a^4`

`5a^4`

Question 2 of 4

Simplify

`sqrt(8x^4)`

`2x^2sqrt2`
`9 sqrt(a)`
`9 sqrt(2a)`
`72 sqrt(a)`

Question 3 of 4

Simplify

`3ysqrt(128y^4)`

`24y^3sqrt2`
`24ysqrt2`
`24ysqrt(2y)`
`8y^3sqrt2`

Question 4 of 4

4. Question
Simplify

`sqrt(9x^2+24xy+16y^2)`
- `3x+4y`
- `3x-4y`
- `4y-3x`
- `7`
Hint

Help Video

Correct

Nice Job!

Incorrect

Multiplication Property of Surds

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

Simplify the surd further

`sqrt(9x^2+24xy+16y^2)` `=` `sqrt((3x+4y)(3x+4y))`

`=` `sqrt((3x+4y)^2)` Apply Exponent Rules

`=` `3x+4y` `(3x+4y)^2` is a perfect square

`3x+4y`

`sqrt(x^4)`	`=`	`(x^4)^(1/2)`
	`=`	`x^2`	Use the Power Rule to simplify `(x^a)^(b)=x^(ab)`

$$\color{#007DDC}{\sqrt{8}}\times\color{#9a00c7}{x^{2}}$$	`=`	`sqrt(4 xx 2)`` xx ``x^2`
	`=`	`sqrt4 xx sqrt2 xx x^2`	Apply the Multiplication Property
	`=`	`2 xx sqrt2 xx x^2`	`4` is a perfect square
	`=`	`2x^2sqrt2`	Rearrange the expression

`sqrt(y^4)`	`=`	`(y^4)^(1/2)`
	`=`	`y^2`	Use the Power Rule to simplify `(x^a)^(b)=x^(ab)`

$$3y\times\color{#007DDC}{\sqrt{128}}\times\color{#9a00c7}{y^{2}}$$	`=`	`3y xx``sqrt(64 xx 2)`` xx ``y^2`
	`=`	`3y xx sqrt64 xx sqrt2 xx y^2`	Apply the Multiplication Property
	`=`	`3y xx 8 xx sqrt2 xx y^2`	`64` is a perfect square
	`=`	`24y^3sqrt2`	Rearrange the expression

Simplify Surds with Variables 2

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Quiz summary

Information

1. Question

Hint

Keep Going!

Multiplication Property of Surds

2. Question

Hint

Well Done!

Multiplication Property of Surds

3. Question

Hint

Correct!

Multiplication Property of Surds

4. Question

Hint

Nice Job!

Multiplication Property of Surds

Quizzes

`sqrt(a^8)`	`=`	`(a^8)^(1/2)`	`x^(1/2)` is the same as `sqrtx`
	`=`	`a^4`	Use the Power Rule to simplify `(x^a)^b = x^(ab)`

`sqrt(9x^2+24xy+16y^2)`	`=`	`sqrt((3x+4y)(3x+4y))`
	`=`	`sqrt((3x+4y)^2)`	Apply Exponent Rules
	`=`	`3x+4y`	`(3x+4y)^2` is a perfect square

	`=`	`5xx``a^4`
	`=`	`5a^4`