Introduction to review on simplifying radicals:
Radicals are nothing but a root that also called as square root. Square root is mentioned with the symbol (sqrt) and sqrt (x). Normally, radicals are rewritten like, sqrt of (a) is rewrite as a (1/2).By the way 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 the review on simplifying radicals in different ways.
Formula for Review on Simplifying Radicals:
General expression with exponent and radical: `n (sqrt (a)) ^m ) =(n (sqrt (a))) ^m =(a1/n) ^m = a^m/n`
Multiplication property for radical expression: `n (sqrt (ab)) = n (sqrt (a)) n (sqrt (b))`
Division property for radical expression: `n (sqrt (a/b)) = (n (sqrt (a))) / (n (sqrt (b)))`
Different forms of radicals is,
A square (second) root is written as `(sqrt(a))` ,
A cube (third) root is written as `^3(sqrt(a))` ,
A fourth root is written as `^4(sqrt(a))` ,
A fifth root is written as: `^5(sqrt(a))` .
I have recently faced lot of problem while learning online math tutor, But thank to online resources of math which helped me to learn myself easily on net.
Example for Review on Simplifying Radicals:
Example for Review on simplifying radicals: `(sqrt (75))`
Given: `(sqrt (75))`
Solution: Given question says, radical (75),
When, we take root for 75 we obtain 25*3.
Because, `sqrt (1225)` = `sqrt (25) sqrt (3)`
= `5 xx sqrt (3)`
Thus we can do Review on simplifying radicals in the prefered way.
Example for Review on simplifying radicals: `^3(sqrt (512))`
Given: `^3(sqrt (512))`
Solution: Given question says, cubic root of (512),
When, we take cubic root for 512 we obtain ( 8 * 8 * 8 )
Because, 8*8*8 = 512
512 = `8^3`
Therefore, cubic root of (512) = `8^3`
= `8` .
Thus we can do Review on simplifying radicals in the prefered way
Given: `(sqrt (81))`
Solution: Given question says, radical of (81),
When, we take square root for 81 we obtain (9 * 9).
Because, 9*9 = 729
81 = `9^2`
Therefore, by simplifying the radical of (81) = `9`
Given: `^4(sqrt (1296))`
Solution: Given question says, cubic root of (1296),
When, we take fourth root for 1296 we obtain 6.
Because, 6*6*6*6 = 1296
1296 = `6^4`
Therefore, by simplifying the fourth root of (1296) = `6`
Given: `^5(sqrt (16807))`
Solution: Given question says, fifth root of (16807),
When, we take fifth root for 3125 we obtain 8.
Because, 7 * 7 * 7 * 7 * 7= 16807
16807 = `7^5`
Therefore, by simplifying fifth root of (16807) = `7`
Radicals are nothing but a root that also called as square root. Square root is mentioned with the symbol (sqrt) and sqrt (x). Normally, radicals are rewritten like, sqrt of (a) is rewrite as a (1/2).By the way 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 the review on simplifying radicals in different ways.
Formula for Review on Simplifying Radicals:
General expression with exponent and radical: `n (sqrt (a)) ^m ) =(n (sqrt (a))) ^m =(a1/n) ^m = a^m/n`
Multiplication property for radical expression: `n (sqrt (ab)) = n (sqrt (a)) n (sqrt (b))`
Division property for radical expression: `n (sqrt (a/b)) = (n (sqrt (a))) / (n (sqrt (b)))`
Different forms of radicals is,
A square (second) root is written as `(sqrt(a))` ,
A cube (third) root is written as `^3(sqrt(a))` ,
A fourth root is written as `^4(sqrt(a))` ,
A fifth root is written as: `^5(sqrt(a))` .
I have recently faced lot of problem while learning online math tutor, But thank to online resources of math which helped me to learn myself easily on net.
Example for Review on Simplifying Radicals:
Example for Review on simplifying radicals: `(sqrt (75))`
Given: `(sqrt (75))`
Solution: Given question says, radical (75),
When, we take root for 75 we obtain 25*3.
Because, `sqrt (1225)` = `sqrt (25) sqrt (3)`
= `5 xx sqrt (3)`
Thus we can do Review on simplifying radicals in the prefered way.
Example for Review on simplifying radicals: `^3(sqrt (512))`
Given: `^3(sqrt (512))`
Solution: Given question says, cubic root of (512),
When, we take cubic root for 512 we obtain ( 8 * 8 * 8 )
Because, 8*8*8 = 512
512 = `8^3`
Therefore, cubic root of (512) = `8^3`
= `8` .
Thus we can do Review on simplifying radicals in the prefered way
Given: `(sqrt (81))`
Solution: Given question says, radical of (81),
When, we take square root for 81 we obtain (9 * 9).
Because, 9*9 = 729
81 = `9^2`
Therefore, by simplifying the radical of (81) = `9`
Given: `^4(sqrt (1296))`
Solution: Given question says, cubic root of (1296),
When, we take fourth root for 1296 we obtain 6.
Because, 6*6*6*6 = 1296
1296 = `6^4`
Therefore, by simplifying the fourth root of (1296) = `6`
Given: `^5(sqrt (16807))`
Solution: Given question says, fifth root of (16807),
When, we take fifth root for 3125 we obtain 8.
Because, 7 * 7 * 7 * 7 * 7= 16807
16807 = `7^5`
Therefore, by simplifying fifth root of (16807) = `7`
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