1. When x is what value, which of the following is meaningful in the real number range?

3-x under (1) radical sign

(2) Divide 1 by 2x- 1 under the root sign.

2. Simplify:

500 under (1) root symbol

(2) 12x under the root sign

(3) 4 under the radical sign and 2/3(4) 2/2 of the square of 3a under the radical sign.

3. Calculation: (1) (24 under the radical sign-one half under the radical sign)-(one eighth under the radical sign+six under the radical sign)

(2) The root number 2 under12 is multiplied by the root number 4 under 3 divided by the root number 5 under 2.

(3) 3+ 6 with 2 times the radical number multiplied by 3- 6 with 2 times the radical number.

(4)(2 root numbers, 48-3 root numbers, 27 times) divided by 6 root numbers.

If the side length of a square is 20 cm, its area is equal to 20 cm.

The rectangular areas with a length of 96cm and a width of 12cm are equal. Find the value of a.

5.

If the lengths of two right-angled sides of a right-angled triangle are 3+ 1 under the square root of 2 and 3- under the square root of 2, respectively.

1, find the length of hypotenuse c.

Comprehensive application

6. When x= 5- 1 under the root sign, find the value of the square of the algebraic expression X +5x-6.

7. As shown in the figure, the cross section of the part consists of rectangle, triangle and sector, with AB=25mm, angle BOC=60 degrees and radius OB= 10mm.

Find the cross-sectional area of this part (accurate to 0. 1 1mm squared. Anyway, you know, let's take 3. 132, and the 3 under the root sign is probably 1.732).

Let me describe it: imagine a rectangle with four letters ABCD in the clockwise direction in the upper left corner, BC is a red dotted line, the other three sides are black BC is an equilateral triangle, and the third point is that O is OB with O as the center.

Circle radius, that's it)

8。 When current passes through a wire, heat is generated. Let the current be I (Ampere), the resistance of the wire be R (Ohm), and the heat generated in t seconds be Q (Joule). According to the physical formula Q=Id multiplied by Rt, if the resistance of the wire is 5 ohms, the wire will generate 30 joules of heat in 1 second, and the value of current I can be obtained (accurate to 0.0 1 amp).

Extension and exploration

9。 It is known that n is a positive integer, and 189n under the root sign is an integer. Find the minimum value of n.

10 Divide the area of a circle with the center o and the radius r into four parts. Please imagine all kinds of segmentation methods as much as possible. If the center of the circle is also point Od, three circles divide the Od area of the great circle into four parts, and find the radius OB of these three circles.

commander

Outer diameter length

1 1. 10 Steel pipes with an outer diameter of 1m are stacked into a triangle similar to a pyramid. In order to prevent rain, it is necessary to build a shelter. What is the minimum height of this shed? (The result is kept to one decimal place).

I've worked hard to fight word by word, and I won't give up biting you to death.