Recourse to quadratic radical operations and methods for solving right triangles

1.Addition and subtraction of quadratic radicals:

First, the quadratic radicals in the formula are reduced to the simplest quadratic radicals, and then the parentheses are removed and the similar quadratic radicals are merged with the addition and subtraction of polynomials.

2.Multiplication of quadratic radicals:

1) Rule: Root A · Root B = Root Ab (A 0 and B 0) 2) Type: i) Single quadratic radical multiplied by single quadratic radical;

ii) a single quadratic radical multiplied by a multiple-second quadratic radical;

iii) multiplying multiple quadratic radicals by multiple quadratic radicals.

When performing multiplication operations, multiplication formulas can sometimes be applied to make the calculation easy.

3.Quadratic radical division:

1) Rule: Root A Root B = Root A B (A 0 and B>0) 2) Type: i) Single quadratic radical divided by single quadratic radical (calculated by applying the algorithm) ii) Multinomial quadratic radical divided by single quadratic radical ** into single quadratic radical divided by single quadratic radical).

iii) The divisor is the sum of two quadratic radicals or the sum of a quadratic radical and a rational number (rationalize the denominator or think by analogy with the operation of the fraction, and reduce the numerator, the common factor in the denominator).

How to solve a right triangle:

1. The groove theorem.

2. Use the similar triangle method.

3. Use the sine and cosine theorems.

Upstairs hungry, he asked about the calculation

Quadratic radicals (I don't know how to play the root number, use words) are all greater than 0:1(root number a) * (root number b) = (root number ab).

Root number a) -3 (root number a) = 3 (root number a) 3(root number a) divided by (root number b) = (root number a b).

3.(root number a b) = (root number ab) b up and down multiplied by root number b at the same time, because there can be no fractions and decimals in the root number 4(root number a) squared = a 5Root number (square of a) = absolute value of a.

6.Another simplification method is (for example): 3 ((root number 3) - (root number 2)) = 3 ((root number 3) + (root number 2)) ((root number 3) - (root number 2)) * root number 3) + (root number 2) = (3 (root number 3) + 3 (root number 2)).

Since there are 2 terms of the quadratic radical formula in the denominator, the denominator should be rationalized by the formula of square difference (a-b)(a+b)=a 2-b 2.

Solve a right-angled triangle: sin=opposite side than hypotenuse cos=adjacent edge than hypotenuse tan=opposite side than adjacent edge cot=adjacent ratio.

Opposite edge: Remember the function value of the special angle: sin30=1, 2, cos30=(root3), 2, tan30=(root3), 3

cot30 = root number 3 (60 degrees is to turn the 30 upside down, and the 30 upside down).

sin45=(root number2) The same goes for root number 2 cos45.

About the formula, there are books. If you have a question, send it up, and everyone will help you solve it.

If you look at the graph, you can see that ab=ac, so d is on the midpoint of BC, which is the point in the upper right corner of the small square at the bottom left (BC passes this point). If the side length of a small square is 1, then the diagonal is root 2, then ad is 2 times the diagonal, which is equal to 2 root 2

Pythagorean theorem: The square of the length of the hypotenuse = the sum of the squares of the length of the two right-angled sides.

The square of the length of the hypotenuse = 7 2 + 4 2

Hypotenuse length = 65 under the root number

According to the Pythagorean theorem.

The square of the hypotenuse = the sum of the squares of the two right-angled sides.

So the hypotenuse is the root number (7 2 + 4 2) = the root number 65

According to the Pythagorean theorem, the length of the hypotenuse is equal to the sum of the squares of the two right-angled sides, so the root number (7*7+4*4) = the root number 65

Root number (7 +4 ) = root number 65 Pythagorean theorem The sum of squares of right-angled sides is equal to the square of hypotenuse.

Pythagorean theorem: The sum of the squares of the two right-angled sides of a right-angled triangle is equal to the square of the third side, a 2 + b 2 = c 2

Let the length of the hypotenuse be c 7 2 + 4 2 = c 2 c = 65 under the root number