The value remains under the radical is 8 ⇒ last answer
Step-by-step explanation:
Let us revise how to write the exponent as a radical
can be written as ![\sqrt[n]{a^{m}}](https://tex.z-dn.net/?f=%5Csqrt%5Bn%5D%7Ba%5E%7Bm%7D%7D)
- To simplify the radical factorize the base "a" to its prime factors
Example:
![(54)^{\frac{2}{3}}=\sqrt[3]{(54)^{2}}](https://tex.z-dn.net/?f=%2854%29%5E%7B%5Cfrac%7B2%7D%7B3%7D%7D%3D%5Csqrt%5B3%5D%7B%2854%29%5E%7B2%7D%7D)
, - Factorize 54 into prime factors ⇒ 54 = 2 × 3 × 3 × 3 =
![\sqrt[3]{(54)^{2}}=\sqrt[3]{[2(3^{3}]^{2}}=\sqrt[3]{2^{2}*3^{6}}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B%2854%29%5E%7B2%7D%7D%3D%5Csqrt%5B3%5D%7B%5B2%283%5E%7B3%7D%5D%5E%7B2%7D%7D%3D%5Csqrt%5B3%5D%7B2%5E%7B2%7D%2A3%5E%7B6%7D%7D)
- 2² can not go out the radical because 2 is less than 3 not divisible by 3
can go out the radical because 6 is divisible by 3, then divide 6 by 3, so it will be 3² out the radical![\sqrt[3]{(54)^{2}}=3^{2}\sqrt[3]{2^{2}}=9\sqrt[3]{4}](https://tex.z-dn.net/?f=%5Csqrt%5B3%5D%7B%2854%29%5E%7B2%7D%7D%3D3%5E%7B2%7D%5Csqrt%5B3%5D%7B2%5E%7B2%7D%7D%3D9%5Csqrt%5B3%5D%7B4%7D)
Now let us solve your problem
∵ ![1250^{\frac{3}{4}}=\sqrt[4]{1250^{3}}](https://tex.z-dn.net/?f=1250%5E%7B%5Cfrac%7B3%7D%7B4%7D%7D%3D%5Csqrt%5B4%5D%7B1250%5E%7B3%7D%7D)
- Factorize 1250 to its prime factors
∵ 1250 = 2 × 5 × 5 × 5 × 5
∴ 
∴ ![\sqrt[4]{(2*5^{4})^{3}}=\sqrt[4]{2^{3}*5^{12}}](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B%282%2A5%5E%7B4%7D%29%5E%7B3%7D%7D%3D%5Csqrt%5B4%5D%7B2%5E%7B3%7D%2A5%5E%7B12%7D%7D)
∵ 2³ can not go out the radical because 3 < 4 and not divisible by it
- 
can go out the radical because 12 can divided by 4
∵ 12 ÷ 4 = 3
∴ can go out the radical as 5³
∴ ![\sqrt[4]{1250}=5^{3}\sqrt[4]{2^{3}}](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B1250%7D%3D5%5E%7B3%7D%5Csqrt%5B4%5D%7B2%5E%7B3%7D%7D)
∴ ![\sqrt[4]{1250}=125\sqrt[4]{8}](https://tex.z-dn.net/?f=%5Csqrt%5B4%5D%7B1250%7D%3D125%5Csqrt%5B4%5D%7B8%7D)
∴ The value remains under the radical = 8
The value remains under the radical is 8
Learn more:
You can learn more about the radicals in brainly.com/question/7153188
#LearnwithBrainly
5 and 6 (5 being the square root of 25 and 6 being the square root of 36, which are the closest perfect squares)
Answer:
Answer B is the correct answer..
cot(theta)=cos(theta)/sin(theta)
Answer:
A.
Step-by-step explanation:
π/4 radians = 45°
In a 45-45-90 degree angle, the ratio of the lengths of the sides is
1 : 1 : √2
x = y = 1/√2
x = y = √2/2
Answer: A.
Answer:
B) x - y = 0
Step-by-step explanation:
The equation for the line shown is y=x. This can be written in general form by subtracting y:
x - y = 0
_____
General form for the equation of a line is ...
ax +by +c = 0
where a, b, c are preferred to be mutually prime integers and a ≥ 0. If a = 0, then b ≥ 0.
