Answer:
x has to be less than 3
Step-by-step explanation:
This is the simplest form
.
<h2>Exponent</h2>
Exponential notation is the form of mathematical shorthand which allows us to write complicated expressions more succinctly. An exponent is a number or letter is called the base. It indicates that the base is to raise to a certain power. X is the base and n is the power.
<h3>Simplification</h3>
Simplification is to make something easier to do or understand and to make something less complicated.
Given
is an expression.
<h3>How to make it simple?</h3>
![\rm 2\sqrt{8x^3} * (3\sqrt{10x^4} - x\sqrt{5x^2} )](https://tex.z-dn.net/?f=%5Crm%202%5Csqrt%7B8x%5E3%7D%20%2A%20%283%5Csqrt%7B10x%5E4%7D%20-%20x%5Csqrt%7B5x%5E2%7D%20%20%29)
On simplifying, we have
![\rm 4\sqrt{2} (x)^{\frac{3}{2}} * ( 3\sqrt{10} x^2 - \sqrt{5} x^{\frac{3}{2}})\\\\24\sqrt{5} x^{\frac{7}{2}} - 4\sqrt{10}x^3\\\\4\sqrt{5}x^3(6\sqrt{x} -\sqrt{2} )\\](https://tex.z-dn.net/?f=%5Crm%204%5Csqrt%7B2%7D%20%20%28x%29%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D%20%2A%20%28%203%5Csqrt%7B10%7D%20x%5E2%20-%20%5Csqrt%7B5%7D%20x%5E%7B%5Cfrac%7B3%7D%7B2%7D%7D%29%5C%5C%5C%5C24%5Csqrt%7B5%7D%20x%5E%7B%5Cfrac%7B7%7D%7B2%7D%7D%20%20-%204%5Csqrt%7B10%7Dx%5E3%5C%5C%5C%5C4%5Csqrt%7B5%7Dx%5E3%286%5Csqrt%7Bx%7D%20-%5Csqrt%7B2%7D%20%29%5C%5C)
This is the simplest form
.
More about the exponent link is given below.
brainly.com/question/5497425
The surface area of the triangular prism is 144 cm²
<u>Explanation:</u>
Given:
Base of the triangle = 4
Height of the triangle = 3
Hypotenuse of the triangle = 5
Length of the prism = 11
Surface area of the rectangular prism = ?
Surface area, A = ![ah + bh + ch + \frac{1}{2} \sqrt{-a^4+2(ab)^2 + 2(ac)^2-b^4 + 2(bc)^2 - c^4}](https://tex.z-dn.net/?f=ah%20%2B%20bh%20%2B%20ch%20%2B%20%5Cfrac%7B1%7D%7B2%7D%20%5Csqrt%7B-a%5E4%2B2%28ab%29%5E2%20%2B%202%28ac%29%5E2-b%5E4%20%2B%202%28bc%29%5E2%20-%20c%5E4%7D)
On substituting the value, we get:
![A = 4 X 11 + 3 X 11 + 5 X 11+\frac{1}{2} \sqrt{-(4)^4 + 2(4X3)^2+2(4X5)^2-3^4 + 2(3X5)^2 - 5^4} \\\\A = 144 cm^2](https://tex.z-dn.net/?f=A%20%3D%204%20X%2011%20%2B%203%20X%2011%20%2B%205%20X%2011%2B%5Cfrac%7B1%7D%7B2%7D%20%5Csqrt%7B-%284%29%5E4%20%2B%202%284X3%29%5E2%2B2%284X5%29%5E2-3%5E4%20%2B%202%283X5%29%5E2%20-%205%5E4%7D%20%5C%5C%5C%5CA%20%3D%20144%20cm%5E2)
Therefore, the surface area of the triangular prism is 144 cm²
Should be -1
I’m never 100% certain of my answers though but I’m pretty sure this is correct