# What is the fastest way to simplify a radical?

Simplify a Radical Expression Using the Product Property
1. Find the largest factor in the radicand that is a perfect power of the index. Rewrite the radicand as a product of two factors, using that factor.
2. Use the product rule to rewrite the radical as the product of two radicals.
3. Simplify the root of the perfect power.

## What is the simplest most radical form?

Expressing in simplest radical form just means simplifying a radical so that there are no more square roots, cube roots, 4th roots, etc left to find. It also means removing any radicals in the denominator of a fraction.

## Is 72 a perfect square?

The square root of 72 is not a whole number and hence, the number 72 is not a perfect square number. The surd form of the square root of 72 is 6√2, where √2 is an irrational number and thus, √72 is also irrational.

## Is 45 a perfect square?

No, 45 is not a perfect square number, since it cannot be written as the product of two equal integers.

## What is the rule for simplifying radicals?

A radical is said to be in simplified radical form (or just simplified form) if each of the following are true. All exponents in the radicand must be less than the index. Any exponents in the radicand can have no factors in common with the index. No fractions appear under a radical.

26 related questions found

### How to solve √?

Long division method
1. Separate your square root base into pairs. ...
2. Find the largest square that divides into the first number or pair. ...
3. Subtract the square from the first number or pair. ...
4. Drop down the next pair. ...
5. Multiply the first digit of the square by two. ...
6. Set up the next factor equation.

Grades 6, 7 and 8 | Math | Middle School | Pre-Algebra - Simplifying and Multiplying Radicals (Part 1)

### How do you know if radicals are simplified?

A radical expression is in its simplest form when three conditions are met:
• No radicands have perfect square factors other than 1.
• No radicand contains a fraction.
• No radicals appear in the denominator of a fraction.

### Why do we simplify radicals?

The short answer is: There are multiple ways of writing the same number, but if we all follow the simplification rules, we'll all write our answers the same way, which makes it easier for people to work together, if they're all expressing their work in the same way.

### How can I calculate fast without a calculator?

1. Addition. The first trick is to simplify your problem by breaking it into smaller pieces. ...
2. Switch. It's often easier to work with adding a smaller number, so instead of 131 + 858, swap the numbers 858 + 131. ...
3. Subtraction. ...
4. Elevens. ...
5. Nines. ...
6. How to solve squares. ...
7. Close together method. ...
8. Simplify Calculations.

### How do radicals work in math?

In maths, a radical is the opposite of an exponent that is represented with a symbol '√' also known as root. It can either be a square root or a cube root and the number before the symbol or radical is considered to be an index number or degree.

### What are the law of radicals?

The laws for radicals are derived directly from the laws for exponents by using the definition a m n = a m n . The laws are designed to make simplification much easier. It is important to reduce a radical to its simplest form.

### What is √9 radical form?

The square root of 9 is equal to 3. It is represented as √9 in radical form and 91/2 in exponential form. When we multiply a number by itself we get the square of the number.

### What grade do you learn √?

As kids progress through the grades, they start learning more and more complex math concepts. Square root and squares are one such topic that kids start learning in grades 4 and 5. But, what are they? the square root of a number is another number, which you get when the original number is multiplied by itself.