Answer:
" A radical expression is an expression containing a square root "
Radical: The √ symbol that is used to denote square root or nth roots.
Radicand: Radicand is a number or expression inside the radical symbol.
WE SAY THAT A SQUARE ROOT RADICAL is simplified, or in its simplest form, when the radicand has no square factors.
A radical is also in simplest form when the radicand is not a fraction.
Example: Simplify radicals [tex]\sqrt{75}[/tex]
Solution: as the radicand i.e. 75 contains a square term since 75=25×3
and we know that [tex]25=(5)^2[/tex]
Hence we take out the square term out of the radical sign to obtain the simplified expression as:
[tex]\sqrt{75}=5\sqrt{3}[/tex].
Example: Simplify [tex]\sqrt{42}[/tex]
solution: as the radicand has the factors as:
[tex]42=2.3.7[/tex]; as it is factored to prime numbers and there is no square term hence the given expression is already simplified.
If the equation has [tex]{n^{th}}[/tex] root, then the simplest form has no factors of [tex]n[/tex].
Further Explanation:
Explanation:
A expression than contain the [tex]{n^{th}}[/tex] root is known as the radical equation.
The symbol of the radical is [tex]\sqrt[n]{x}.[/tex]
The radicand is a number that is in the radical.
The examples of the radical are as follows,
Consider the expression as [tex]\sqrt {36}[/tex]
The simplest form of the expression is 6.
The radical expression is square root of 36.
The radicand is 36.
Now consider the expression as [tex]\sqrt[3]{{27}}.[/tex]
The simplest form of the expression is 3.
The radical expression is cube root of 27.
The radicand is 27.
If the equation has [tex]{n^{th}}[/tex] root, then the simplest form has no factors of [tex]n[/tex].
Learn more:
Answer details:
Grade: High School
Subject: Mathematics
Chapter: Exponents and Powers
Keywords: radical expression, expression, factors, simplest form, square root, radicand, cube root, constant term.
