Square Root

Let Us Learn About Square Root

To find the square root of a given number is to think of what number when multiplied by itself is equal to the given number.

For example, to find the square root of 4, we have to think of a number that when multiplied by itself gives 4. The number is 2 since 2 × 2 = 4.

So the square root of a given number is the positive number whose square produces the given number.

Properties of Square Roots:

• The product of two values in the square roots with different numbers inside it can be written in a single root in a product of those two root values.
• The number outside the square root symbol, when it gets into square root, it turns into a square of number.
• The square root of fraction value can be written as individual roots, as root in numerator and root in denominator separately.
• When a perfect square comes out of the square root symbol, it becomes the number without square root.

Square root is an radical symbol which is used in the mathematics. It is shown as the symbol as √. The number inside the radical symbol is called as the rubicund, for example if the given value is √x. The x is called as the rubicund which is the number inside the radical symbol √. There are more number of roots available depending upon the value we have. The roots are square root √x, cube root 3√x, Fourth root 4√x this up to nth root n√x. Here we are going to see about the square root of 16 and 17 in different methods of solving.

Let’s make it clear with some examples:

• √x * √y = √xy [By the first property]
• = x√y = √x2y [By the second property]
• √x/ y = √x/√y [By the third property]

Explain Ray in Geometry

Let us study about Ray,

A ray is also a piece of a line, except that it has only one endpoint and continues forever in one direction. It could be thought of as a half-line with an endpoint. It is named by the letter of its endpoint and any other point on the ray. The symbol → written on top of the two letters is used to denote that ray. This is ray AB (Figure 1).

Figure1 Ray AB.

It is written as

This is ray CD (Figure 2 ).

Figure 2 Ray CD.

It is written as or

Note that the nonarrow part of the ray symbol is over the endpoint.

Hope the above explanation helped you.

square root of complex number

Let us learn about square root,

A divisor of a quantity that when squared gives the quantity. For example, the square roots of 25 are 5 and -5 because 5 × 5 = 25 and (-5) × (-5) = 25.

A number that, when squared, yields a given number. For example, since 5 × 5 = 25, the square root of 25 (written 25) is 5.

"Roots" (or "radicals") are the "opposite" operation of applying exponents; you can "undo" a power with a radical, and a radical can "undo" a power. For instance, if you square 2, you get 4, and if you "take the square root of 4", you get 2; if you square 3, you get 9, and if you "take the square root of 9", you get 3:

Hope the above explanation helped you.

distance formula in coordinate geometry

Let us study about distance formula in coordinate geometry,

In Figure, A is (2, 2), B is (5, 2), and C is (5, 6)

Finding the distance from A to C.

To find AB or BC, only simple subtracting is necessary.

AB = 5 − 2 and BC = 6 − 2 AB = 3 BC = 4

To find AC, though, simply subtracting is not sufficient. Triangle ABC is a right triangle with AC the hypotenuse. Therefore, by the Pythagorean Theorem,

If A is represented by the ordered pair ( x₁, y₁) and C is represented by the ordered pair ( x₂, y₂), then AB = ( x₂ − x₁) and BC = ( y₂ − y₁).

Then

This is stated as a theorem.

Theorem: If the coordinates of two points are ( x₁, y₁) and ( x₂, y₂), then the distance, d, between the two points is given by the following formula (Distance Formula).

Example 1: Use the Distance Formula to find the distance between the points with coordinates (−3, 4) and (5, 2).

Example 2: A triangle has vertices A(12,5), B(5,3), and C(12, 1). Show that the triangle is isosceles.

By the Distance Formula,

Because AB = BC, triangle ABC is isosceles.

Hope the above explanation helped you.

Circle and line Intersectionhttp://www.blogger.com/img/blank.gif

Let us learn about circle and line intersection,
So, let us consider a circle and a line PQ. There can be three possibilities given
in Fig. below:
In Fig. (i), the line PQ and the circle have no common point. In this case,
PQ is called a non-intersecting line with respect to the circle. In Fig.(ii), there
are two common points A and B that the line PQ and the circle have. In this case, we
call the line PQ a secant of the circle. In Fig.(iii), there is only one point A which
is common to the line PQ and the circle. In this case, the line is called a tangent to the
circle.