Known: M = 1 / 3, n = 1 / 27, find the value of the root number M-N of the root sign M-N + the root sign m-2 times the root sign N + m + 4n-4 times the root sign Mn Hurry!

If you break sentences better, you can't understand the back. Is that double the root n or the molecular position?
Normally, I think using the square difference formula:
(radical m-radical n) * (radical m + radical n) = M-N

Given that M = 1 / 3 and N = 1 / 27, find the root number m minus the root number M-N of the root number n plus the root number m minus 2 root sign n% m + 4n-4 root sign Mn

(m-n) / (m-n) / (m-n) / (M + 4n-4 √ Mn) / (M + 4n-4 √ Mn) / (V √ m-2 √ n) = ((v-m-2 √ n) = ((m-4-n-4 √ Mn) / ((v-m-2 √ n) + ((v-m-2 √ n) = (m-m-2 √ n) = m-m-3 √ n = n = 3 / 3, n = 27, the original formula = 2 √ 1 / 3-3-3 √ 3-3 √ 3-3 √ 3 3 √ 2 3 V √ M-3 v-3 √ M-3 1 / 27 = 2 / 3 √ 3-1 / 3 √ 3 = 1 / 3 √ 3

Positive numbers m and N satisfy m + 4 times root mn-2 times root sign M-4 times root sign N + 4N = 3. Find the value of root number m + 2 times root number n + 2002 cent root number m + 2 times root number n-8 Because I don't know how to type the math format, I'd like to write the questions according to the text

According to your narration, the title should be known m + 4 (MN) ^ 0.5-2m ^ 0.5-4n ^ 0.5 + 4N = 3, and the value of (m ^ 0.5 + 2n ^ 0.5-8) / (m ^ 0.5 + 2n ^ 0.5 + 2002) (^ is the sign of the power, and 0.5 times the power is the opening root sign). If the title is such, then it should take the m ^ 0.5 + 2n ^ 0.5 as a whole to calculate, assuming that m ^ 0.5 + 2n ^ 0.5 = t = t, the topic is known T ^ 2-2t = 3, seek (solve) (solve) (2-2t = 3, seek (solve) (solve) (2-2t = 3), seek (solve) (solve) (2-2t = 3), seek (2 T-8) / (T + 2002), I don't need to say the rest?

Cube root of root 26 / 27 minus 1 Thank you

The cube root of √ [(26 / 27) - 1]
=-Cube root of [√ (1 / 27)]
=-√ [(cube root of (1 / 27)]
=-√（1/3）
=-（√3）/3
Opening cube roots before square roots is the same effect as square roots first and then cube roots

It is known that M is the integer part of Radix 19 and N is the fractional part of Radix 19. Find the cube root of M-N ^ 2-8 times Radix 19 + 32

M=4
(n = (4) - 19
M-N ^ 2-8 * radical 19 + 32
4 - (19-8 root number 19 + 16) - 8 root number 19 + 32
4-19 + 8 root number 19-16-8 root number 19 + 32
4-19-16+32
=1
Cube root is 1

Cube root 26 / 27 - 1 cube root plus square root (1 - 5 / 4)

Cube root and cube are reciprocal operations

Estimate the size of the following numbers: 1) root 40 and 6.26, 2) cube root of 20 and 7 / 2, 3) root 50 and 7, 4) root sign 5-1 and 1 / 6

6.26²=39.1876<40
So √ 40
（7/2）³=343/8>160/8=20
So the cube root of 7 / 2 > 20
7²=49<50
So √ 50 > 7
√5>√4=2
(√5-1)>2-1=1
(√5-1)/6>1/6

Given vector a = (cos3 / 2x, SIN3 / 2x), vector b = (cos1 / 2x, - sin1 / 2x), X ∈ [- π / 8, π / 4]. (1) find vector a · vector b (inner product) and vector a + vector B; (2) if f (x) = vector a · vector B - vector a + vector B, find the maximum value of F (x)

(1)
A.B
=(cos(3x/2),sin(3x/2)).(cos(x/2),-sin(x/2))
=cos(3x/2).cos(x/2)- sin(3x/2).sin(x/2)
=cos2x
(2)
|a+b|^2
=(cos(3x/2)+cos(x/2))^2+ (sin(3x/2)-sin(x/2))^2
= 2 + 2(cos(3x/2)cos(x/2)- sin(3x/2)sin(x/2) )
=2 + 2cos2x
= 2 + 2[2(cosx)^2 -1)]
|a+b| =2cosx
f(x) = a.b-|a+b|
= cos2x- 2cosx
= 2(cosx)^2-2cosx -1
= 2(cosx-1/2)^2 -3/2
min f(x) at cosx =1/2
min f(x) = -3/2

Given the vector a = (cos3 / 2x, SIN3 / 2x), B = (cos1 / 2x, - sin1 / 2x), X belongs to [- π / 8, π / 4], find a · B and | a + B|

A.B
=(cos(3x/2),sin(3x/2)).(cos(x/2),-sin(x/2))
=cos(3x/2).cos(x/2)- sin(3x/2).sin(x/2)
=cos2x
|a+b|^2
=(cos(3x/2)+cos(x/2))^2+ (sin(3x/2)-sin(x/2))^2
= 2 + 2(cos(3x/2)cos(x/2)- sin(3x/2)sin(x/2) )
=2 + 2cos2x
|a+b| =√(2 + 2cos2x)

Vector a = (cos3 / 2x, SIN3 / 2x) vector b = (cos1 / 2x, sin1 / 2x), X {0, π] (1) When x = π / 4, the value of vector a · vector B and | vector a + vector B | (2) find the maximum value of F (x) = m | vector a + vector B | vector a · vector b (m |)

Is the absolute value in these two questions? Or brackets? I calculated the absolute value to find a · B. It is very simple to use the formula of "remainder plus positive" to simplify the result to cosx, that is √ 2 / 2, and | a + B | is to square the formula and square the result to | a + B | = a |

Known: M = 1 / 3, n = 1 / 27, find the value of the root number M-N of the root sign M-N + the root sign m-2 times the root sign N + m + 4n-4 times the root sign Mn Hurry!