Simplifying Radical Examples

Simplifying Radicals

Simplifying radicals include the simplification of radicals denominator before performing basic mathematical operation.

Radical is a topic from Algebra which relates with the exponents. This topic includes simplification of radicals, multiplying and dividing radicals and solving radicals. Lets us find answers for radical examples in order to understand the concept of radicals.

Radical Examples

Example 1: Find the principal cube root of 125.

Solution:

125 = 5³.

Hence, the principal cube root of 125 is 5.

One more numerical on simplifying radical example.

Example 2: Rationalize the denominator of √(15/3).

Solution:

We have to rationalize the denominator, √3.

The rationalizing factor is √3.

Multiply the numerator and denominator by √3

[√(15/3)] X [√3/√3]

Now we have,

[√(15 x 3)]/(√3)^2

(√45)/3


Hence, we have rationalized the denominator.

Area of Triangle Problem

Area of triangle formula is given as 1/2 x b x h, where b is the base of the triangle and h is the height of the triangle. A triangle is a geometrical figure which consists of three sides, in which one of the side is considered as base and the altitude in other words is called as height of the triangle.

Area of triangle does not change with types of triangle, formula remains the same. As types of triangle depends on sides measurements and also with angles, like for example if a triangle has two equal sides is called as isosceles triangle.

Triangle problem : Calculating area of equilateral triangle of 6cm.
Solution :
As per the area of triangle formula,
to calculate we need b and h, given b = 6cm,
h = √(3^2+6^2)
= √(9+36)
=√45
= √5x9
= 3√5 is the height (As per Pythagoras theorem)

So area is calculated as
1/2 x b x h
= 1/2 x 6 x 3√5
= 9√5 Sqcm.