simplifying square roots

1) find volume of this prism?
v=bwh

b=√12"
w=√6"
h=√8"

2)simplify: √576

3)simplify: √400

4)simplify: √256

5)simplify: √(1/4)

2.) 24

3.) 20
4.) 16
5.) 0.5

hope I was a help! :) going through the same class right now, so I hear ya'

1.) 24 :)

no it's not like that

for ex 2√5 + 6√5= 8√5

the answer has to be in √

To simplify square roots, we need to find the factors of the number inside the square root that are perfect squares. Here's how you can simplify each of the given square roots:

1) To find the volume of a prism, you multiply the base area (b) by the height (h). In this case, the base area (b) is given by √12", the width (w) is √6", and the height (h) is √8". To simplify this expression, we need to multiply the numbers inside the square roots that have the same radicand (number inside the square root).

b = √12" = √(4 * 3) = √4 * √3 = 2√3"
w = √6"
h = √8" = √(4 * 2) = √4 * √2 = 2√2"

The volume (v) of the prism is then:

v = b * w * h = (2√3")(√6")(2√2") = 4√3" * √6" * √2" = 4√(3 * 6 * 2) = 4√(36) = 4 * 6 = 24 cubic inches.

So, the volume of the prism is 24 cubic inches.

2) To simplify √576, we need to find the perfect square factors. The perfect square factors of 576 are 16 and 36.

√576 = √(16 * 36) = √16 * √36 = 4 * 6 = 24.

So, √576 simplifies to 24.

3) The perfect square factors of 400 are 16 and 25.

√400 = √(16 * 25) = √16 * √25 = 4 * 5 = 20.

So, √400 simplifies to 20.

4) The perfect square factor of 256 is 16.

√256 = √(16 * 16) = √16 * √16 = 16 * 16 = 16.

So, √256 simplifies to 16.

5) To simplify √(1/4), we first simplify the fraction inside the square root.

√(1/4) = √1 / √4

Since the square root of 1 is 1 and the square root of 4 is 2, we have:

√(1/4) = 1/2.

So, √(1/4) simplifies to 1/2.