how to work this problem step by step

Question

√18

Answer 1

If you're just trying to solve the radical, keep in mind that you can break apart the number inside of it. Or rather, you can turn one radical into one radical times another. This is good place to demonstrate mathematical equivalence at the level of an individual term.

 

Let's start with this: We have √18; this is the same as (18)^½, or eighteen to the one-half power. At some level, this is the same as any conventional number, because, well, it's a real number! So, like any conventional number, it can be broken apart so long as its value remains the same. Getting straight to the point, we break √18 into √9√2, just like we can break the normal number 18 into 9 times 2. We know that √9 = 3, so the final equation looks like:

 

√18 = 3√2

 

Recall that I mentioned mathematical equivalence: most any problem you are asked to solve will be an equation (obviously), so one side will equal the other. √18 is approximately 4.243, as is 3√2. Mathematical equivalence is relevant for an entire equation, or just a part of it. Again, recall that we first broke the radical up into two separate radicals, and then further simplified one radical into a simple whole number.

 

There's more to this, depending on what you're doing or what you're dealing with. If something's still not clear, please feel free to ask.

Answer 2

√18  ----->√9 * 2

 

we notice that 9 is a perfect square. so we take the square root of 9 outside the radical and the 2 remains inside the radical:

 

±3√2