Question

How do you know if a Radical Expression is in simplest form?

Answer 1

If the equation has ${n^{th}}$ root, then the simplest form has no factors of $n$.

Further Explanation:

Explanation:

A expression than contain the ${n^{th}}$ root is known as the radical equation.

The symbol of the radical is $\sqrt[n]{x}.$

The radicand is a number that is in the radical.

The examples of the radical are as follows,

Consider the expression as $\sqrt {36}$

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 $\sqrt[3]{{27}}.$

The simplest form of the expression is 3.

The radical expression is cube root of 27.

The radicand is 27.

If the equation has ${n^{th}}$ root, then the simplest form has no factors of $n$.

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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.

Answer 2

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 $\sqrt{75}$

Solution: as the radicand i.e. 75 contains a square term since 75=25×3

and we know that $25=(5)^2$

Hence we take out the square term out of the radical sign to obtain the simplified expression as:

$\sqrt{75}=5\sqrt{3}$.

Example: Simplify $\sqrt{42}$

solution: as the radicand has the factors as:

$42=2.3.7$; as it is factored to prime numbers and there is no square term hence the given expression is already  simplified.