Introduction on how to solve simple radicals:
In math a radical is defined as a number with a square root or a cube root. The symbol for the radical is the root symbol. The square root and the cube root operations are common on math and it becomes mandatory to learn the basics of solving simple radicals. The root symbol is called as a radical sign while the numbers inside the root sign is called as radicals. Let’s see more on this topic.
More on how to solve simple radicals:
As said before the numbers in root sign are together called as radicals. The number indicating the square root or cube root is called as an index. While simplifying the radicals we have to learn the properties in simplifying then,
1. The product property.
`sqrt (a*b)` = `sqrt a` * `sqrt b`
2. The Quotient Property.
`sqrt (a/b)` = `sqrt a /sqrt b`
While simplifying a number we should break the number into the largest perfect square factor and the other factor. Then both the factors go under the root sign. Take square root of the perfect square number and leave the other number inside the root sign.
In division type the same method shown above is applied for the numerator and denominator. If there is a number with root sign in the denominator then multiply both numerator and denominator by that root number and simplify.
I have recently faced lot of problem while learning cbse latest sample papers, But thank to online resources of math which helped me to learn myself easily on net.
Example problems on how to solve simple radicals:
1. Simplify the radical √180
Solution:
The number 180 can be written as 36 x 5. Since 36 has a perfect square.
`sqrt 180` = `sqrt (36* 5)`
By the product property,
`sqrt (36*5)` = √36 x√5 = 6√5
`sqrt 180` = 6 √5
2. Simplify the radical √ (8/45)
Solution:
The number 8 can be written as 4 x 2. Since 4 has a perfect square.
The number 45 can be written as 9 x 5. Since 9 has a perfect square.
`sqrt [(4*2)/(9*5)]`
By the Quotient Property,
`sqrt [(4*2)/ (9*5)]` = `sqrt (4*2) /sqrt (9*5)`
= 2√2/3√5
To simplify this we multiply both numerator and denominator by √5
= `(2*sqrt 2*sqrt 5)/(3*sqrt 5*sqrt 5)`
=`(2sqrt10)/15`
Practice problems on how to solve simple radicals:
1. Simplify the radical `sqrt 112`
Answer: 4√7
2. Simplify the radical `sqrt (25/32)`
Answer: 5√2/8
In math a radical is defined as a number with a square root or a cube root. The symbol for the radical is the root symbol. The square root and the cube root operations are common on math and it becomes mandatory to learn the basics of solving simple radicals. The root symbol is called as a radical sign while the numbers inside the root sign is called as radicals. Let’s see more on this topic.
More on how to solve simple radicals:
As said before the numbers in root sign are together called as radicals. The number indicating the square root or cube root is called as an index. While simplifying the radicals we have to learn the properties in simplifying then,
1. The product property.
`sqrt (a*b)` = `sqrt a` * `sqrt b`
2. The Quotient Property.
`sqrt (a/b)` = `sqrt a /sqrt b`
While simplifying a number we should break the number into the largest perfect square factor and the other factor. Then both the factors go under the root sign. Take square root of the perfect square number and leave the other number inside the root sign.
In division type the same method shown above is applied for the numerator and denominator. If there is a number with root sign in the denominator then multiply both numerator and denominator by that root number and simplify.
I have recently faced lot of problem while learning cbse latest sample papers, But thank to online resources of math which helped me to learn myself easily on net.
Example problems on how to solve simple radicals:
1. Simplify the radical √180
Solution:
The number 180 can be written as 36 x 5. Since 36 has a perfect square.
`sqrt 180` = `sqrt (36* 5)`
By the product property,
`sqrt (36*5)` = √36 x√5 = 6√5
`sqrt 180` = 6 √5
2. Simplify the radical √ (8/45)
Solution:
The number 8 can be written as 4 x 2. Since 4 has a perfect square.
The number 45 can be written as 9 x 5. Since 9 has a perfect square.
`sqrt [(4*2)/(9*5)]`
By the Quotient Property,
`sqrt [(4*2)/ (9*5)]` = `sqrt (4*2) /sqrt (9*5)`
= 2√2/3√5
To simplify this we multiply both numerator and denominator by √5
= `(2*sqrt 2*sqrt 5)/(3*sqrt 5*sqrt 5)`
=`(2sqrt10)/15`
Practice problems on how to solve simple radicals:
1. Simplify the radical `sqrt 112`
Answer: 4√7
2. Simplify the radical `sqrt (25/32)`
Answer: 5√2/8
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