What are the values of root 1 to root 10

What are the values of root 1 to root 10

Root 1 = 1
Root 2 = 1.414
Root 3 = 1.732
Root 4 = 2
Radical 5 = 2.236
Root 6 = 2.449
Root 7 = 2.646
Root 8 = 2.828
Root 9 = 3
Root 10 = 3.162

What's the root
1+√2-1

We don't need to work out the root sign here. The result is the root sign 2
The root sign has the opposite meaning to square. For example, the root sign 9 equals 3

Given the function f (x) = ax ^ 2 - | x-a | when a > 0, find the minimum value of function f (x) in the interval [0, + ∞)

When x ≥ a, f (x) = ax & # 178; - x + a = a [X-1 / (2a)] &# 178; + A-1 / (4a)
When 1 / (2a) is in this interval, that is, 0 = - A, a > = √ 2 / 4
The results are as follows
When 0

There is a kind of relationship between the phone call cost y (yuan) and the call time x (min), which can be approximately expressed as y = 5 + 0.25x
(1) Xiao Zhang gave 100 points. How much is the fee?
(2) Xiao Zhang's phone bill this month is 55 yuan. How many points has he made?

1, y = 5 + 0.25 × 100 = 30 yuan
2, 55 = 5 + 0.25x, x = 200 minutes
Which school and what grade are you in?

As shown in the figure, in the right angle trapezoid ABCD, ad is parallel to BC, ∠ a = 90 ° AB = ad = 1 / 2BC, and m and N are the midpoint of AD and CD respectively, connecting BM, Mn and BN
Determine the shape of △ BMN

The isosceles right angle △ link AC ∵ m is the midpoint of AD, ab = ad ∵ am = AB / 2 ∵ AB = BC / 2 ∵ am: ab = AB: BC ∵ a = 90 °, AD / / BC ∵ ABM ∵ ABC ∵ BM: AC = 1:2 ∵ basc = ∵ AMB ∵ basc + ∵ CAD = 90 ∵ CAD + ∵ AMB = 90 ⊥ AC ⊥ BM ∵ m, n is ad, CD

It is known that there are six protons and six neutrons in the nucleus of a carbon atom, the mass of which is 1.993 * 10 to the - 26th power kg, and there are six protons and six neutrons in the nucleus of a chlorine atom
There are 17 protons and 18 neutrons, and their mass is 5.8933 * 10 ^ - 26kg. Two different methods are used to calculate the relative atomic mass of chlorine atom (the calculation result retains one decimal place), and explain which calculation result is more accurate

Method 1: 17 + 18 = 35
Method 2: 5.8933 * 10 ^ - 26kg * 12 / 1.993 * 10-26kg = 35.5
So the second method is more accurate!

Car a and car B start from both places at the same time and travel in opposite directions. The distance is 900 km. The speed ratio of car a and car B is 2:3. After six hours of meeting, what are the speeds of car a and car B respectively?

900 △ 6 = 150 (km), 2 + 3 = 5150 × 25 = 60 (km), 150 × 35 = 90 (km); a: the speed of car a is 60 km / h, and that of car B is 90 km / h

If the two sides of a triangle are 8cm and 5cm long, the longest of the third side is () cm

According to the sum of the two sides of the triangle is greater than the third side, so the third side should be less than 13,

Given ABC ∈ positive integer, ABC = 1, and a (1 + C) > 1, B (1 + a) > 1, C (1 + b) > 1, try to prove 2 (a + B + C) ≥ 1 / A + 1 / B + 1 / C + 3

It is known that a, B, C > 0, ABC = 1, and a (1 + C) > 1, B (1 + a) > 1, C (1 + b) > 1
Verification: 2 (a + B + C) ≥ 1 / A + 1 / B + 1 / C + 3
From a, B, C > 0, ABC = 1, let a = x / y, B = Y / Z, C = Z / x, where x, y, z > 0
The inequality is 2 (x / y + Y / Z + Z / x) ≥ Y / x + Z / y + X / Z + 3
It is equivalent to 2 (X & # 178; Z + Y & # 178; X + Z & # 178; y) ≥ X & # 178; y + Y & # 178; Z + Z & # 178; X + 3xyz
Substituting a = x / y, C = Z / x into a (1 + C) > 1 leads to x + Z > y (Y > 0), that is, X-Y + Z > 0
Similarly, Y-Z + x > 0 and z-x + Y > 0 can be obtained from B (1 + a) > 0 and C (1 + b) > 0, respectively
So 4 (X & # 178; Z + Y & # 178; X + Z & # 178; y) - 2 (X & # 178; y + Y & # 178; Z + Z & # 178; x) - 6xyz = (X-Y + Z) (X-Y) & # 178; + (Y-Z + x) (Y-Z) & # 178; + (z-x + y) (z-x) & # 178; ≥ 0
That is, there are 2 (X & # 178; Z + Y & # 178; X + Z & # 178; y) ≥ X & # 178; y + Y & # 178; Z + Z & # 178; X + 3xyz
Note: the last step of formula is a little abrupt, which is actually based on the conditions of equal sign and known conditions

Two people lift a wooden stick of 20cm in length and 200N in thickness at both ends to find: (1) the gravity of the stick; (2) how far is the center of gravity of the stick from the thick end?

(1) No matter where the stick is pulled, the gravity is equal to the pull
So g = F1 + F2 = 300 + 200 = 500N
(2) The center of gravity of the stick is the origin
According to the lever principle F1 L1 = F2 L2
And L2 = 20 - L1
That is 300 L1 = 200 (20-l1)
The solution is L1 = 8 cm
The left side uses more force, so the left side is 8cm away from the thick end