1- Simplify the radical expression: √250h^4k^5

a) hk√125
b) 5√10h^4k^5
c) 5h^2k^2√10k
d) 25hk√10k **

2- Simplify the radical expression: √21y * 5√49y
a) 5y√1,029
b) 5√1,029y^2
c) 35y√21
d) 35√21y^2 **

3- Simplify the radical expression: √20x^13y^5 / 5xy^7 (this whole fraction is a square root, not just the nominator, this is the same for all the fractions in this question with the √ sign)
a) √4x^12 / y^2
b) 2x^6 / y **
c) 2√x^12 / y^2
d) 2x^6y

4- Simplify the radical expression: 5√7 + 2√175
a) 7√182
b) 15√14
c) 7√175
d) 15√7 **

5- Simplify the radical expression by rationalizing the denominator
√8 / √6x
a) 2√3x / 3x
b) 2√2x / x **
c) √6x / 3x
d) 4√3x / 3x

PLS HELP

factor out perfect squares.

#1. √250h^4k^5 = √25*10*h^4*k^4*k = √(25h^4k^4)*10k = 5h^2k^2 √10k
#2. wrong again. You don't factor them all out
#3. ok
#4. ok
#5. nope. √8*6x = √48x = 4√3x ...

1- 5h^2k^2 √10k

2- 35y√21
3- 2x^6 / y
4- 15√7
5- √6x / 3x

I changed 1, 2, and 5. Are these right? For #2 my original answer was 5√1,029y^2 but I'm pretty sure I got it wrong.

#1,2 ok

For #5, √8 / √6x = √48x / 6x = 4√3x / 6x = 2√3x / 3x

Oh I see now.

Thanks Mr. oobleck!

I'm here to help! Let's go through each question one by one:

1- Simplify the radical expression: √250h^4k^5
To simplify this expression, we can break down 250 into its prime factors: 250 = 2 * 5^2. We can also break down h^4k^5 as h^2 * h^2 * k^2 * k^3. Taking the square root of the factors, we get √250h^4k^5 = √(2 * 5^2 * h^2 * h^2 * k^2 * k^3). Simplifying this, we get 5hk^2√2k, so none of the options listed match.

2- Simplify the radical expression: √21y * 5√49y
To simplify this expression, we can simply multiply the numbers in front of the square roots and the numbers inside the square roots. 5√49y simplifies to 5 * 7√y = 35√y, so the expression becomes √21y * 35√y = 35√(21y^2). None of the options listed match.

3- Simplify the radical expression: √20x^13y^5 / 5xy^7
To simplify this expression, we can simplify the numerator and denominator separately. √20x^13y^5 = √(4 * 5 * x^12 * y^4 * y) = 2x^6y^2√5y. We can simplify the denominator as 5xy^7 = 5xy^2 * y^5 = 5xy^2y^2y^2y. Simplifying this, we get √20x^13y^5 / 5xy^7 = (2x^6y^2√5y) / (5xy^2y^2y^2y) = 2x^6 / y. The correct option is b) 2x^6 / y.

4- Simplify the radical expression: 5√7 + 2√175
To simplify this expression, we cannot directly combine the square roots because they have different radicands. However, we can break down 175 into its prime factors: 175 = 5^2 * 7. We can simplify 5√7 as √(5^2 * 7) = 5√7. Therefore, the expression becomes 5√7 + 2√(5^2 * 7) = 5√7 + 10√7 = 15√7. The correct option is d) 15√7.

5- Simplify the radical expression by rationalizing the denominator: √8 / √6x
To rationalize the denominator, we multiply both the numerator and denominator by the conjugate of the denominator: √8 / √6x * √6x / √6x = √(8 * 6x) / (√6x * √6x) = √48x / 6x = √(16 * 3x) / 6x = (4√3x) / 6x = 2√3x / 3x. The correct option is b) 2√2x / x.

I hope this helps! Let me know if you have any other questions!

Sure, I'd be happy to help you with these questions. Let's go through each one step by step:

1- Simplify the radical expression: √250h^4k^5

To simplify this expression, we need to look for perfect square factors of the number under the square root. In this case, we can break down 250 into its prime factorization: 2 * 5 * 5 * 5.

Now we can simplify the square root as follows:
√250h^4k^5 = √(2 * 5 * 5 * 5 * h^4 * k^5)

Group the perfect squares together:
= 5 * h^2 * k^2 * √(2 * 5)

Simplify the radical:
= 5h^2k^2√10

Therefore, the answer is c) 5h^2k^2√10.

2- Simplify the radical expression: √21y * 5√49y

To simplify this expression, we can multiply the numbers outside the square root and the numbers inside the square root separately.

√21y * 5√49y = 5√(21y) * √(49y)

Multiply the numbers outside the square root:
= 5 * √(21y)

Multiply the numbers inside the square root:
= 5 * √(21 * y * y)

Simplify the square root:
= 5 * √(21) * √(y * y)

= 5 * √(21) * y

Therefore, the answer is b) 5√21y^2.

3- Simplify the radical expression: √20x^13y^5 / 5xy^7

To simplify this expression, we can simplify the numerator and denominator separately and then divide.

√20x^13y^5 / 5xy^7 = (√(20) * √(x^13) * √(y^5)) / (5xy^7)

Simplify the square root of 20:
= (√(4 * 5) * √(x^13) * √(y^5)) / (5xy^7)

Take out the perfect square from the square root of x^13:
= (2x^6 * √(5) * √(x) * √(y^5)) / (5xy^7)

Simplify the square root of y^5:
= (2x^6 * √(5) * √(x) * y^2) / (5xy^7)

Cancel out common factors:
= (2x^6 * √(5) * y^2) / (5x * y^7)

Simplify the expression:
= (2x^5 * y * √(5)) / (5 * y^6)

= 2x^5 * y / (5 * y^6) * √(5)

= 2x^5 / (5 * y^5) * √(5)

Therefore, the answer is b) 2x^6 / y.

4- Simplify the radical expression: 5√7 + 2√175

To simplify this expression, we need to simplify each radical separately and then add them together.

5√7 + 2√175 = 5√(7) + 2√(5 * 5 * 7)

= 5√7 + 2 * 5√7

= 5√7 + 10√7

= (5 + 10)√7

Therefore, the answer is d) 15√7.

5- Simplify the radical expression by rationalizing the denominator: √8 / √6x

To rationalize the denominator, we need to multiply both the numerator and the denominator by the conjugate of the denominator.

√8 / √6x = (√8 * √6x) / (√6x * √6x)

= √(8 * 6x) / (√6x)^2

= √(48x) / (6x)

= √(16 * 3 * x) / (6x)

= (4√3 * √x) / (6x)

= (2 * 2√3 * √x) / (6x)

= (4√3 * √x) / (6x)

Simplify the expression:
= 2√3x / 3x

Therefore, the answer is b) 2√2x / x.

I hope this helps! Let me know if you have any further questions.