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Simplify Radicals Calculator

Simplify Radicals Calculator

Select the operation and provide the required entities. The calculator will simplify the radicals accordingly, with the steps shown.

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Expression

$$ a\sqrt[n]b$$

$$ a\sqrt[n]b+c\sqrt[m]d=?$$

$$ a\sqrt[n]b.c\sqrt[m]d=? $$

$$ \frac{a\sqrt[n]b}{c\sqrt[m]d}=? $$

a (Optional)

b

n

c (Optional)

d

m

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Table of Content

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Determine the simplest radical form of any number or expression with the assistance of this free online simplify radicals calculator.

What about going through the context below to know more about the mathematics of radicals?

Keep Scrolling!

What Is Radical?

“The symbol \(\sqrt\) that can be used to represent either square root or nth root is called a radical.”

simplify

Mathematically:

$$ y . \sqrt[n]{x} $$

Where:

  • \(\sqrt\) is the radical symbol
  • x is the radicand
  • n represents the nth root of the radicand enclosed under the expression

Gone are the days when simplifying radicals was a complicated task. Now this free simplify radical calculator can do this for you within a few moments with accurate outputs. How does it sound?

When it comes to decimal radicals with exponents, we have another decimal calculator that makes it possible for you to divide the decimal exponents.

Operations on The Radicals:

Let us have a look at the arithmetic operations on the radicals.

Addition of The Radical Expressions:

You can only add two radicals if the radicands involved and the number of the roots are the same. In case they are not the same, first try to simplify and make them the same and then add them as per the rule is defined. Moreover, the free adding radicals calculator can also get it done within a few simple clicks.

$$ a \sqrt[n]{b} + c \sqrt[m]{d} $$

$$ n=m $$
$$ b=d $$

Subtraction of the Radical Expressions:

The rule for the subtraction of the radicals is the same as it is for the addition. The only thing that is changed here is the negative sign instead of addition among the radicals. But in case you find it difficult to simplify, the free adding and subtracting radicals calculator will do that for you in a span of seconds.
$$ a \sqrt[n]{b} – c \sqrt[m]{d} $$

$$ n=m $$
$$ b=d $$

Multiplication of the Radical Expressions:

Multiplication of the radicals is simpler enough. All you have to do is just multiply the radicands together if and only if the order of the root is the same. Just as:

$$ a \sqrt[n]{b} * c \sqrt[m]{d} $$

$$ \left(a*c\right) \sqrt[nm]{bd} $$

Same rule is followed by our best multiplying radicals calculator to find the product of two radicals instantly.

If in case we have the following expression with different roots i.e;
$$ n ≠ m $$

Then we can not find the product of the radical expressions.

Division of The Radical Expressions:

Division of the radicals involves the cancellation of the same radicals and reducing them to the most simplified form.
If,

$$ n=m $$

Then we have:

$$ \frac{a \sqrt[n]{b}}{c \sqrt[m]{d}} $$

Division of radicals may confuse you a little bit. But you do not need to worry as the dividing radicals calculator will assist you right away to simplify division problems at the very moment. Whatever the operation you want to perform on any radical or expressions like that, this simplifying radical expressions calculator will get it done immediately.

Rules To Simplify Radicals:

Whenever simplifying radicals, you need to keep in mind couple of rules as listed below:

  • The nth root must be larger than the number 2 or equal to it
  • The radicand must be a positive number and not a negative number

Our free simplify radical calculator strictly takes into account both of these rules to simplify any radical expression.

Square Root:

Square roots are the radicals of the order 2. If the nth root becomes 2 in a radical expression, it is known as the square root. You can also simplify the square root by using our free square root calculator which is another suitable approach. But as it can also be done with this simplest radical form calculator, you can use it as well to explore the under root raised to the second power.

In actuality, square roots are the inverse operations that are raised to the power of two against the number.

For example:

Consider the number 25. Its square root will be \(\sqrt{25}\). On the other hand, the square of 5 yields 25 i.e; \(5^{2} = 25\). As we see that this is a simpler number. But if in case there comes a bigger number just like 14444, it becomes difficult to find square root manually. This is where our best simplifying radicals calculator comes to aid you straightaway.

How To Simplify Radical Expressions?

Here we will be resolving a couple of examples that involve the application of the arithmetic operations on the radical expressions. Let’s have a look!

Example # 01:
Add the following radical expressions:

$$ \sqrt{75} + \sqrt{12} $$

Solution:

As we see that the radicands in the expressions are not the same. So first we will try to make them identical as follows:

$$ \sqrt{75} + \sqrt{12} $$
$$ \sqrt{25*3} + \sqrt{4*3} $$
$$ 5\sqrt{3} + 2\sqrt{3} $$

Now the radicands and root order are the same, we can add them as:

$$ 5\sqrt{3} + 2\sqrt{3} $$
$$ 7\sqrt{3} $$

Example #02:
Find the product of the following radical expressions:

$$ \sqrt{18} * \sqrt{14} $$

Solution:

So here we have:

$$ \sqrt{9*2} * \sqrt{14} $$

As the square root of 9 is 3, we have:

$$ \sqrt{9*2} * \sqrt{14} $$
$$ 3\sqrt{2} * \sqrt{14} $$
$$ 3\sqrt{28} $$
$$ 3\sqrt{4*7} $$
$$ 3*2\sqrt{7} $$
$$ 6\sqrt{7} $$

Which is our final answer that could also be verified by using a free simplify radicals calculator.

Example # 03:
Simplify the following radical below:

$$ 228 $$

Solution:

As the given number is even, so it can be divided by 2 which is the simplest

$$ 228 = 2*144 $$

Factors of 144:
$$ 2*57 $$

Factors of 57:
As 57 can not yield a perfect square, so it will be written as it is under the radical sign.
As 2 is multiplied two times with 144 and 57, respectively, so it will come outside as it completes the square.

$$ 228 = 2\sqrt{57} $$

Which is our required answer. In case of any doubt, let our best solving radical equations calculator fade it away and satisfy you by calculating most simplified radical equations.

How Simplify Radicals Calculator Works?

This radical simplify takes a span of moments to generate the accurate simplified form of a number or radical expression. Let’s find how!

Input:

  • From the first drop-down list, make a selection of what operation you want to adopt for radical simplification
  • After doing so, write down all the required numbers in their designated fields
  • Now tap the calculate button

Output:
The free simplify radical expression calculator calculates:

  • The most simplified radical form
  • Displays if the radical is not simplifiable

FAQ’s:

What is the square root of 288 in radical form?

The square root of the given number 288 is \(12\sqrt{2}\). The simplify radicals calculator also goes for displaying the same results by saving you a lot of time.

How do you reverse the radical form?

To reverse the radical operation, you need to find the square root to that power. The actual thirst of the expression is to find that number which when multiplied by itself, will yield the actual number inside the radicand. With the use of the free simplify radicals calculator, you can also get an idea about the number that will result in the same number by multiplying it with itself.

Can you take a square root of 0?

Yes, the square root of 0 is 0.

Can roots be negative?

Yes, you can determine the square root of negative numbers. The negative sign under the radical sign is itself a representation of the complex number iota that separates out leaving behind the positive number.

For example:
$$ \sqrt{-4} $$
$$ = \sqrt{-1} \sqrt{4} $$
$$ = \sqrt{4}\iota $$
$$ =2\iota $$

How do you write 2 cubed?

Cube means three times. So the cube of 2 is determined as below:
$$ 2^{3} = 2*2*2 $$
$$ 2^{3} = 8 $$

Why is 1729 a magic number?

According to mathemagicians, 1729 is considered a magical number because we can express this number as the sum of the cubes of the two different sets of numbers.

Are radicals the same root as Radicands?

First of all, we know that the radicals that have the same roots and radicands are known as the like radicals. For such radicals, you have to consider the radicals as the variables. Every time when you think of adding or subtracting radicals, you need to consider them to be added or subtracted as variables.

Conclusion:

So far we discussed the use of the simplest radical form calculator to determine the most reduced form of any radical. Except under root of the second power, you can reduce each and every high power root at the very instant by using this free simplify radicals calculator. We hope you find this article guide very helpful.

References:

From the source of wikipedia: Solution in radicals

From the source of khan academy:Radical equations & functions, Domain of a radical function

From the source pof lumen learning: Radical Equations, Identify Extraneous Solutions, Square Roots and Completing the Square, Completing the Square to Solve a Quadratic Equation, Use the Quadratic Formula to Solve Quadratic Equations