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من طرف Admin الإثنين أكتوبر 25, 2010 2:20 amIntroduction to radical number:
The radical symbol was introduced by John Bell in 1668. Radicals having the same properties as the properties of the numbers. A radical is an expression that expresses the symbol with square roots, cube roots etc. Radical is the word that comes from the Latin word Radix. When we use the radical without a sign or index number, it mentions the positive square root of the radicand.
Radical Number:definition
In radicals have square root, cubic root, and nth root. Square root has a root of degree 2. Cubic root has a root of degree 3 and nth root has a root of degree n number. Roots are using the radical symbol
n = x
It is also defined as complex numbers, and complex roots of 1 in higher mathematics
Square root and Cubic roots :
The real number has the one positive root and one negative root, for example square roots of 36 are 6 and -6. The other name of positive square root is principal square root and mentioned the radical sign. √16 = 4 and cubic can be written as = 4
The negative numbers have square root of imaginary number is two. For example, square root of -16 is 4i and -4i
Here, i = or i2 = -1
Identities and properties:
= × ,
= ( ) / ( )
The simplification of the exponent form
m = ( ) m = (a1/n) m = am/n
× = -1 where as = 1
Redical Number:multiplying and Dividing Rules
Multiplying and Dividing rule for Radical:
The following rule can be used to multiplying and dividing the radicals,
Multiplying rule dividing rule
√a √b = √ (a b) ; =
For example,
√8 .√4 =√32 ; √8 /√4 =√ (8/4)
We can also write it as,
(
(1/2). (4)(1/2)= (32) (1/2) ; ( (1/2) / (4) (1/2) = (8/4) (1/2)
The most important thing when we multiply radicals is, both radical must have the common index.
Consider the another example
((1/3) (4)(1/2) ; ( (1/3) / (4) (1/2)
We cannot multiply and divide the above radicals. Because both having different index
Examples:
1. Multiply the radical numbers: √14 and √8
(√14) (√ = √ (14 ×
= √ (14 × 2 × 4)
= √ (28 × 4)
= √(7×4) √4
= 4√7
Answer: The simplification of given radical numbers 4√7
2. Multiply the radical numbers: (√ 9x3) (3√-15x4)
(√ 9x3) (3√-15x4) = (√ 9x3. 3√-15x4)
= (3x√x 3x2√-15)
= 9 x3√ (-1)15x we know, √ (-1) = i
= i 9 x3 √15x -1 = i2
Answer: The simplification of given radical numbers i 9 x3 √15x
The radical symbol was introduced by John Bell in 1668. Radicals having the same properties as the properties of the numbers. A radical is an expression that expresses the symbol with square roots, cube roots etc. Radical is the word that comes from the Latin word Radix. When we use the radical without a sign or index number, it mentions the positive square root of the radicand.
Radical Number:definition
In radicals have square root, cubic root, and nth root. Square root has a root of degree 2. Cubic root has a root of degree 3 and nth root has a root of degree n number. Roots are using the radical symbol
n = x
It is also defined as complex numbers, and complex roots of 1 in higher mathematics
Square root and Cubic roots :
The real number has the one positive root and one negative root, for example square roots of 36 are 6 and -6. The other name of positive square root is principal square root and mentioned the radical sign. √16 = 4 and cubic can be written as = 4
The negative numbers have square root of imaginary number is two. For example, square root of -16 is 4i and -4i
Here, i = or i2 = -1
Identities and properties:
= × ,
= ( ) / ( )
The simplification of the exponent form
m = ( ) m = (a1/n) m = am/n
× = -1 where as = 1
Redical Number:multiplying and Dividing Rules
Multiplying and Dividing rule for Radical:
The following rule can be used to multiplying and dividing the radicals,
Multiplying rule dividing rule
√a √b = √ (a b) ; =
For example,
√8 .√4 =√32 ; √8 /√4 =√ (8/4)
We can also write it as,
(
(1/2). (4)(1/2)= (32) (1/2) ; ( (1/2) / (4) (1/2) = (8/4) (1/2)The most important thing when we multiply radicals is, both radical must have the common index.
Consider the another example
(
(1/3) (4)(1/2) ; ( (1/3) / (4) (1/2) We cannot multiply and divide the above radicals. Because both having different index
Examples:
1. Multiply the radical numbers: √14 and √8
(√14) (√
= √ (14 × = √ (14 × 2 × 4)
= √ (28 × 4)
= √(7×4) √4
= 4√7
Answer: The simplification of given radical numbers 4√7
2. Multiply the radical numbers: (√ 9x3) (3√-15x4)
(√ 9x3) (3√-15x4) = (√ 9x3. 3√-15x4)
= (3x√x 3x2√-15)
= 9 x3√ (-1)15x we know, √ (-1) = i
= i 9 x3 √15x -1 = i2
Answer: The simplification of given radical numbers i 9 x3 √15x
