How do you calculate the half power of three?

How do you calculate the half power of three?

Square root of mental arithmetic
The square root of 4 is 2
Then, the square root of 3 can be estimated first: 2
Calculation: (2 + 3 / 2) / 2 = 1.75
Then, by substituting 1.75
(1.75+3/1.75)/2=(1.75+1.714)/2=1.732
Find the square root of a
Estimate: X
x'=(x+a/x)/2
x=x'
The square root of a can be obtained by iteration

Calculate: (64 of 49) to the minus half power Isn't it 8 / 7

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1 / 2 of 27 = ± 3 √ 3

How to calculate the half power of a number? For example: One half of 4 is（ The value of (x ^ 2 + 1) / x?

That is to square this number
2? 2 = 4, 1 / 2 of 4 = 2
(X^2+1)/x =x+1/x
1 / 8 of x) = 1 / 2
If both sides of the equation are squared at the same time
x+1/x+2=64
x+1/x=62
∴ (X^2+1)/x =62

What about the minus third power of 11

=1 / 11 to the 1 / 3 power
=1 / (cube root of 11)

What about the fourth power of minus one third

(-1/3)^4=1/3^4=1/81

Calculate: (minus one third) to the fifth power × the seventh power of six times the sixth power of (negative half)

（-1/3）^5（6）^7（-1/2）^6
=（-1/3）^5（-1/2）^6（6）^7
=(1/6)^5(-1/2)(6^5)(6^2)
=(1/6)^5(6^5)(6^2)(-1/2)
=1^5X36X（-1/2）
=-18

What is (minus 0.125) to the 12th power (minus one has two thirds) to the seventh power (minus eight) to the thirteenth power (minus three fifths) to the ninth power

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The 12th power of - 0.125 = how many - the 7th power of - 5 / 3 = how many - the 9th power of - 3 / 5 = how much

（-0.125）∧12=2∧（-36）

Calculation: the 2nd power of 2002 - 2001 * 2003

2002²-2001*2003
=2002²-（2002-1）*（2002+1）
=2002²-（2002²-1）
=1