Answer:
![4\sqrt[3]{2}x(\sqrt[3]{y}+3xy\sqrt[3]{y} )](https://tex.z-dn.net/?f=4%5Csqrt%5B3%5D%7B2%7Dx%28%5Csqrt%5B3%5D%7By%7D%2B3xy%5Csqrt%5B3%5D%7By%7D%20%29)
Step-by-step explanation:
Let's start by breaking down each of the radicals:
![\sqrt[3]{16x^3y}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B16x%5E3y%7D)
Since we're dealing with a cube root, we'd like to pull as many perfect cubes out of the terms inside the radical as we can. We already have one obvious cube in the form of 
, and we can break 16 into the product 8 · 2. Since 8 is a cube root -- 2³, to be specific, we can reduce it down as we simplify the expression. Here our our steps then:
![\sqrt[3]{16x^3y}\\=\sqrt[3]{2\cdot8\cdot x^3\cdot y}\\=\sqrt[3]{2} \sqrt[3]{8} \sqrt[3]{x^3} \sqrt[3]{y} \\=\sqrt[3]{2} \cdot2x\cdot \sqrt[3]{y} \\=2x\sqrt[3]{2}\sqrt[3]{y}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B16x%5E3y%7D%5C%5C%3D%5Csqrt%5B3%5D%7B2%5Ccdot8%5Ccdot%20x%5E3%5Ccdot%20y%7D%5C%5C%3D%5Csqrt%5B3%5D%7B2%7D%20%5Csqrt%5B3%5D%7B8%7D%20%5Csqrt%5B3%5D%7Bx%5E3%7D%20%5Csqrt%5B3%5D%7By%7D%20%5C%5C%3D%5Csqrt%5B3%5D%7B2%7D%20%5Ccdot2x%5Ccdot%20%5Csqrt%5B3%5D%7By%7D%20%5C%5C%3D2x%5Csqrt%5B3%5D%7B2%7D%5Csqrt%5B3%5D%7By%7D)
We can apply this same technique of "extracting cubes" to the second term:
![\sqrt[3]{54x^6y^5} \\=\sqrt[3]{2\cdot27\cdot (x^2)^3\cdot y^3\cdot y^2} \\=\sqrt[3]{2}\sqrt[3]{27} \sqrt[3]{(x^2)^3} \sqrt[3]{y^3} \sqrt[3]{y^2}\\=\sqrt[3]{2}\cdot 3\cdot x^2\cdot y \cdot \sqrt[3]{y^2} \\=3x^2y\sqrt[3]{2} \sqrt[3]{y}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B54x%5E6y%5E5%7D%20%5C%5C%3D%5Csqrt%5B3%5D%7B2%5Ccdot27%5Ccdot%20%28x%5E2%29%5E3%5Ccdot%20y%5E3%5Ccdot%20y%5E2%7D%20%5C%5C%3D%5Csqrt%5B3%5D%7B2%7D%5Csqrt%5B3%5D%7B27%7D%20%5Csqrt%5B3%5D%7B%28x%5E2%29%5E3%7D%20%5Csqrt%5B3%5D%7By%5E3%7D%20%5Csqrt%5B3%5D%7By%5E2%7D%5C%5C%3D%5Csqrt%5B3%5D%7B2%7D%5Ccdot%203%5Ccdot%20x%5E2%5Ccdot%20y%20%5Ccdot%20%5Csqrt%5B3%5D%7By%5E2%7D%20%5C%5C%3D3x%5E2y%5Csqrt%5B3%5D%7B2%7D%20%5Csqrt%5B3%5D%7By%7D)
Replacing those two expressions in the parentheses leaves us with this monster:
![2(2x\sqrt[3]{2}\sqrt[3]{y})+4(3x^2y\sqrt[3]{2} \sqrt[3]{y})](https://tex.z-dn.net/?f=2%282x%5Csqrt%5B3%5D%7B2%7D%5Csqrt%5B3%5D%7By%7D%29%2B4%283x%5E2y%5Csqrt%5B3%5D%7B2%7D%20%5Csqrt%5B3%5D%7By%7D%29)
What can we do with this? It seems the only sensible thing is to look for terms to factor out, so let's do that. Both terms have the following factors in common:
![4, \sqrt[3]{2} , x](https://tex.z-dn.net/?f=4%2C%20%5Csqrt%5B3%5D%7B2%7D%20%2C%20x)
We can factor those out to give us a final, simplified expression:
Not that this is the same sum as we had at the beginning; we've just extracted all of the cube roots that we could in order to rewrite it in a slightly cleaner form.
Answer:
9
Step-by-step explanation:
3*3=9
ABC and 123
A1 B1 C1 A2 B2 C2 A3 B3 C3
Answer:
x= 1/4k + −11/4
Step-by-step explanation:
4x+11=k
Step 1: Add -11 to both sides.
4x+11+−11=k+−11
4x=k−11
Step 2: Divide both sides by 4.
4x/4 = k−11/4
x=1/4k + −11/4
Answer:
x=1/4k + −11/4
OR
If you are solving for K:
Let's solve for k.
4x+11=k
Step 1: Flip the equation.
k=4x+11
Answer:
k=4x+11
10:10 because you subtract 1 hour and 30 mins from the original time<span />
The length of rectangle is 139 inches
Solution:
Given that, area of the rectangle is 3197 square inches
Let "L" be the length of rectangle and "W" be the width of rectangle
Also given that rectangle has the length of 22 inches less than 7 times the width
Length = 7 times width - 22
L = 7W - 22
<em><u>The area of rectangle is given as:</u></em>
Substituting the values we get,
On solving the above quadratic equation using quadratic formula,
Substituting in above quadratic formula,
Since width of rectangle cannot be negative, ignore negative value of "W"
So width W = 23 inches
Length L = 7W - 22 = 7(23) - 22 = 139 inches
Thus length of rectangle is 139 inches
