Whether there is a positive integer n, is 1 / (root sign 3N + 2) is a rational number If so, give a value of N. if not, give the reason It can be said that the radical sign 3N + 2 = a 3n+2=a^2 n=(a^2-2)/3 And then what do you say?

There is no such number
There are only three cases in which any positive integer is divided by 3: remainder 0, 1, 2
Then the square of the corresponding positive integer and the remainder divided by 3 are: remainder 0, 1, 1
But 3N + 2 is divided by 3 and the remainder is 2
Therefore, 3N + 2 must not be a complete square number, then 1 / radical (3N + 2) must not be a rational number
In other words, for all positive integers n, 1 / radical (3N + 2) is not rational
See your supplement
n=(a^2-2)/3
A ^ 2 | 3 = 0 or 1
A ^ 2-2 = 1 or 2
So n is not an integer

It is known that (M + n-2) 2 and the root sign 2m-3n-4 are opposite numbers to each other. Find the square root of m-5n

According to the meaning of the question, the equation is obtained
(M + n-2) 2 + root sign (2m-3n-4) = 0
According to the meaning of the square sum and the number of the square root, it is concluded that
m+n-2＝0①
2m-3n-4＝0②
① X 2 - 2, n = 0
Substituting n = 0 into ① gives m = 2
So m = 2, n = 0, substituting it under the root sign (m-5n) yields
Under root sign (2-5 × 0) = root 2
The square root of m-5n is root 2
Finish it!

Simplify the result of Radix 2 divided by (Radix 2-1) As the title

Original formula = √ 2 (√ 2 + 1) / (√ 2-1) (√ 2 + 1)
=(2+√2)/(2-1)
=2+√2

First simplify and then evaluate, A-2 / A-4 divided by [a + (4 / A-4)], where a = radical 3 + 2

The original formula = (A-2) / (A-4) / (A-4)
=(a-2)/(a-4)×(a-4)/(a-2)²
=1/(a-2)
=1/(√3+2-2)
=√3/3

S = 3 / radical 7-2, s = radical 7 + 2

s=3(√7+2)/[(√7+2)(√7-2)]
=3(√7+2)/(7-4)
=3(√7+2)/3
=√7+2

Simplification: (2 root sign 3-2) (3 root sign 6 + root 2) (root 12-root 63) (2 root sign 7 + 3 root sign 3) It's a simple way, not an answer

Are you sure there's a simple way to do this? I'll first put forward the root sign 2 of the second term, and then multiply the first two terms by the root sign 2 * (2 root sign 3-2) (3 root sign 3 + 1) to get the root sign 2 * (16-4 root sign 3) and the last two terms. The third term becomes (2 root sign 3-3 root sign 7), and then multiply the fourth term to get (2 root sign 3-3 root sign 7) *

Simplify the sum of Radix 3 plus Radix 5 divided by 3 minus Radix 6 minus Radix 10 plus Radix 15

(√3+√5)/(3-√6-√10+√15)
=(√3+√5)/[√3(√3-√2)+√5(√3-√2)]
=(√3+√5)/(√3-√2)(√3+√5)
=1/(√3-√2)
=(√3+√2)/(√3-√2)(√3+√2)
=√3+√2

Simplify 1. (with sign 3 + root 5) divided by (3-radical 6-radical 10 + radical 15) 2.2 Radix 6 divided by (radical 2 + Radix 3 + Radix 5)

One
denominator
3-√6-√10+√15
=√3（√3-√2）+√5（√3-√2）
=（√3+√5）（√3-√2）
The numerator / denominator can be eliminated √ 3 + √ 5 to obtain 1 / (√ 3 - √ 2)=
√3+√2
2 numerator and denominator at the same time * (√ 2 + √ 3 - √ 5)
The denominator gives exactly 2 √ 6
It's just going to eliminate the molecules,
The results were √ 2 + √ 3 - √ 5

Simplification: 3 + Radix 6 divided by 5 Radix 3-2 Radix 12 - Radix 32 + Radix 50

3 + root 6 divided by 5 root 3-2 root 12 - root 32 + root 50
=3+√2/5-4√3-4√2+5√2
=3-4√3+6√2/5;
It's my pleasure to answer your questions and skyhunter 002 to answer your questions
If there is anything you don't understand, you can ask,

Reduce the root 5 / 2 divided by the root 84 times the root 7 / 16

Original formula = √ (5 / 2) × √ 84 × √ (16 / 7)
=√(5/2÷84×16/7)
=√(5/2×1/84×16/7)
=√(10/147)
=√(30×1/49×1/9)
=√30×1/7×1/3
=(√30)/21

Whether there is a positive integer n, is 1 / (root sign 3N + 2) is a rational number If so, give a value of N. if not, give the reason It can be said that the radical sign 3N + 2 = a 3n+2=a^2 n=(a^2-2)/3 And then what do you say?