Radicals are nothing but a root which we also called square root. Square root is indicated with the symbol (sqrt) and sqrt (). Normally, radicals are rewrite like, sqrt of (a) is rewrite as a (1/2). Likewise radicals are expressed in various forms. The expression sqrt (8) is read as “radical eight”, or “the square root of eight”. Thus, we are going to see how to rewrite radicals in different ways.
Formula for how to rewrite radicals:
Formula for how to rewrite radicals:
General expression with exponent and radical:
`( ^nsqrt (a) ) ^m` = `( ^nsqrt (a) ) ^m` = `(a1/n) ^m ` = `am/n`
Multiplication property for radical expression: ( `^nsqrt (ab)` ) = ( ` ^nsqrt (a)` ) ( ` ^nsqrt (b)` )
Division property for radical expression: ( `^nsqrt (a/b)` ) = ( `^nsqrt (a)` ) / ( `^nsqrt (b)` )
Different forms of radicals is,
A square (second) root is written as ( ` sqrt(x)` )
A cube (third) root is written as ( `^3sqrt(x)` ),
A fourth root is written as ( `^4sqrt(x)` ),
A fifth root is written as: ( ` ^5sqrt(x)` ).
Example for how to rewrite radicals:
Example for how to rewrite radicals: Rewrite radical(`sqrt (1225)` )
Given: (`sqrt (1225)` )
Solution: Given question says, radical (1225),
When, we take radical for 1225, we obtain 25*49.
Because, ( `^nsqrt (ab)` ) = ( ` ^nsqrt (a)` ) ( ` ^nsqrt (b)` )
`sqrt (1225)` = `sqrt (25)` `sqrt (49)`
= `sqrt(5)` * `sqrt(7)`
`sqrt (1225)` = `35`
Thus, we can do how to rewrite radicals in the prefered way.
Example for how to rewrite radicals: Rewrite radical( `^3sqrt (512)` )
Given: ( `^3sqrt (512)` )
Solution: Given question says, cubic root of (512),
When, we take cubic root for 512, we obtain 8.
Because, `8*8*8 = 512`
`^3sqrt(512)`` =` `8^3`
Therefore, cubic root for (512) = 8^3
Thus,we can do how to rewrite radicals in the prefered way
Example for how to rewrite radicals: Rewrite radical `^3sqrt (729)`
Given: (`^3sqrt (729)` )
Solution: Given question says, cubic root of (729),
When, we take cubic root for 729, we obtain 9.
Because, `9*9*9 = 729`
`^3sqrt(729) = 9^3`
Therefore, cubic root of (729) = 9^3
Example for how to rewrite radicals: Rewrite radical `^4sqrt (1296)`
Given: (`^4sqrt (1296)` )
Solution: Given question says, fourth root of (1296),
When, we take fourth radical for 1296, we obtain 6.
Because, `6*6*6*6 = 1296`
`^4sqrt(1296 )= 6^4`
Therefore, fourth root of (1296) = 6^4
Example for how to rewrite radicals: Rewrite radical `^5sqrt (3125)`
Given: (`^5sqrt (3125)` )
Solution: Given question says, fifth root of (3125),
When, we take Fifth radical for 3125, we obtain 8.
Because, `5*5*5*5*5 = 3125`
`^5sqrt(3125) = 5^5`
Therefore, fifth root of (3125) = 5
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