Simplify Radicals 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

Help Video

Correct

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Incorrect

Multiplication Property of Radicals

`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 Radicals

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

Simplify the radical 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 Radicals with Variables 2

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Quiz summary

Information

1. Question

Hint

Keep Going!

Multiplication Property of Radicals

2. Question

Hint

Well Done!

Multiplication Property of Radicals

3. Question

Hint

Correct!

Multiplication Property of Radicals

4. Question

Hint

Nice Job!

Multiplication Property of Radicals

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`