How to simplify radicals?
A radical is also known as a 'Square root' of a number. The objective is to get the radical to it's lowest term.
First you'll have to know the basic perfect squares:
After you've acknowledged those you can simplify radicals.
âˆš9 = 3
âˆš64 = 8
âˆš81 = 9
âˆš8 = ?
8 is not a perfect square so you will need to use factors.
âˆš8 = âˆš4 times âˆš2
Then you know that 4 is a perfect square and simplifies to 2.
Your answer will be 2 âˆš2.
There are three steps on how to evaluate a radical. Some of the step-by-step instructions are multiply two radicals with the same index number by simply multiplying the numbers beneath the radicals, divide a radical by another radical with the same index number by simply dividing the numbers inside, and simplify large radicals using the product and quotient rules of radicals.
You can only subtract (or add) radicals if they are to the same base. In that case, you treat the radical part as you would a letter-variable in an algebraic expression. So, just as 5x - 3x = 2x you have 5âˆš2 - 3âˆš2 = 2âˆš2. Sometimes, you may to simplify the radicals to make the bases equal. For example: 3âˆš8 - 4âˆš2 = 6âˆš2 - 4âˆš2 = 2âˆš2
The question is based on the premise that It is not possible to simplify a radical without first factorising it. That is simply not true. Beginners may find it a useful step but that does not make it "important to always factor". Simplifying radicals entails removing square factors of the radicand from under the radical. This can be done without factoring first.