subject: Solving Algebra Problems Radical [print this page] A radical is an expression and it expresses the square roots, cube roots etc. The word radicl comes from the Latin word Radix, and algebra comes from Arabic language. Generally radical is also called Root. Algebra is also deals with common statements of relations, to represent specific sets of numbers, vectors, values etc, Radicals having the same properties as the properties of the numbers. When we use the radical without a sign or index number, it mentions the positive square root of the radical.
Laws of Indices in Radical:
Product law: If m and n are positive integer , a != 0
1.) am an = am+n
2.) am an = am-n
Identities and properties:
root(n)(ab) = root(n)(a) root(n)(b)
root(n)((a/b)) = root(n)(a) / root(n)(b)
root(n)(a)m = ( root(n)(a) )m = (a1/n )m = am/n
Solving Algebra Problems:
Solving algebra problem 1: v(3/50xy2 )
Sol : Step 1: multiply and divide dy 2x
v(3/50xy2 ) = v((32x) / (50xy2 2x))
Step 2: multiply the variables and numbers
= v(6x / 100x2y2 )
Step 3: square root of 100x2y2 = 10xy
so, Answer for the given algebra problem is = (1/10xy) v6x
Solving algebra problem 2: v(a2/b5c7)
Sol : Step 1: multiplies and divides by bc
v(a2/b5c7) = v(a2 bc / b5c7 bc)
Step 2: multiply the variable with exponent
= v(a2 bc / b6c8 )
Step 3: Square root of a2b6c8 = ab3c4
So, Answer for the given algebra problem is = (a / b3c4 )v bc
The radical form is an expression which is under the symbol square root. The expression contains multiplication, fraction, addition, subtraction. The simplified radical form is to simplify the given expression in simplified form. The simplified radical form contains the symbol square root in the numerator but not in the denominator.
Example Problems- Simplified Radical Form:
Change the expression sqrt(x^3/x) in simplified radical form.
Given, the expression is sqrt(x^3/x)
The sqrt(x^3) can be written assqrt(x^2 * x)
The sqrt(x^2 * x) is same as sqrt(x^2) * sqrt(x) .
So the given expression would be sqrt(x^2) *sqrt(x) / x.
The sqrt(x^2) is same as sqrt(x^(2*1/2)) which is equal to x 2 * 1 / 2.
The answer in the numerator is x*sqrt(x) .
The expression is equal to x*sqrt(x) / x
The answer is sqrt(x)
Change the expression sqrt((x+1)^3) /(x+1) in simplified radical form.
Given, the expression is sqrt((x+1)^3) )/(x+1).
The sqrt((x+1)^3) can be written as sqrt((x+1)^2 * (x+1))
The sqrt((x+1)^2 * (x+1)) is same as sqrt((x+1)^2) * sqrt((x+1)) .
So the given expression would be sqrt((x+1)^2) * sqrt((x+1)) / (x+1).
The sqrt((x+1)^2) is same as (x+1)2 1/2 which is equal to( x+1) 2 * 1 / 2.
The answer in the numerator is (x+1)*sqrt(x+1) .
The expression is equal to (x+1)*sqrt(x+1) /( x+1)
The answer is sqrt(x+1) .
More Example Problems - Simplified Radical Form:
Change the expression sqrt((x+2)^3/(x+2)) in simplified radical form.
Given, the expression is sqrt((x+2)^3/(x+2)) .
The sqrt((x+2)^3) can be written as sqrt((x+2)^2 * (x+2))
The sqrt((x+2)^2 * (x+2)) is same as sqrt((x+2)^2) * sqrt((x+2)) .
So the given expression would be sqrt((x+2)^2) * sqrt((x+2)) / (x+2).
The sqrt((x+2)^2) is same as (x+2)2)1/2 which is equal to( x+2) 2 * 1 / 2.
The answer in the numerator is (x+2)*sqrt(x+2) .
The expression is equal to (x+2)*sqrt(x+2) /sqrt(x+2)
The answer is x+2 .
Change the expression sr((x+3)3 )/(x+3) in simplified radical form.
Given, the expression is sqrt((x+3)^2) /(x+3).
The sqrt((x+3)^3) can be written as sqrt((x+3)^3) * (x+3))
The sqrt((x+3)^3) *( x+3)) is same as sqrt((x+3)^2) * sqrt((x+3)) .
So the given expression would be sqrt((x+3)^2) * sqrt((x+3)) / (x+3).
The sqrt((x+3)^2) is same as (x+3)2)1/2 which is equal to( x+3) 2 * 1 / 2.
The answer in the numerator is (x+3)*sqrt((x+3))
The expression is equal to (x+3)*sqrt((x+3)) /( x+3)
