Square root,ratio & Proportion,percentage

A square root of a number is a value that, when multiplied by itself, gives the number.

Example: 4 × 4 = 16, so a square root of 16 is 4.


Note that (−4) × (−4) = 16 too, so −4 is also a square root of 16.


The symbol is √ which always means the positive square root.

Example: √36 = 6 (because 6 x 6 = 36)

the ratio defines the relationship between two quantities such as a:b, where b is not equal to 0. A ratio can be written as a fraction, say 2/5. the ratio can be represented in three different forms, such as:

• a to b
• a : b
• a/b

Proportion is an equation that defines that the two given ratios are equivalent to each other. In other words, the proportion states the equality of the two fractions or the ratios. In proportion, if two sets of given numbers are increasing or decreasing in the same ratio, then the ratios are said to be directly proportional to each other. Ratio and proportions are said to be faces of the same coin. When two ratios are equal in value, then they are said to be in proportion. In simple words, it compares two ratios. Proportions are denoted by the symbol  ‘::’ or ‘=’.

The proportion can be classified into the following categories, such as:

• Direct Proportion
• Inverse Proportion
• Continued Proportion
• the formula for ratio is defined as;
• a: b ⇒ a/b

Proportion Formula:-

 a/b = c/d or  a : b :: c : d

              Difference Between Ratio and Proportion

To understand the concept of ratio and proportion, go through the difference between ratio and proportion given here.

1. Ratio is used to compare the size of two things with the same unit where as The proportion is used to express the relation of two ratios.

2.Ratio is expressed using a colon (:), slash (/) where as proportion  is expressed using the double colon (::) or equal to the symbol (=).

3.Ratio  is an expression where as proportion is an equation.

Percentage, a relative value indicating hundredth parts of any quantity. One percent (symbolized 1%) is a hundredth part; thus, 100 percent represents the entirety and 200 percent specifies twice the given quantity. Percentages are often used to express a proportionate part of a total. The percent value is computed by multiplying the numeric value of the ratio by 100.

50% of 40% is 50/100 × 40/100 = 0.50 × 0.40 = 0.20 = 20/100 = 20%.