## anonymous 5 years ago how do you u simplify the radical expression 98

1. anonymous

$\sqrt{98}=\sqrt{2}*\sqrt{49} = 7\sqrt{2}$

2. anonymous

I imagine that after answering a bunch of these it becomes automatic but what is the strategy for breaking one of these down?

3. anonymous

The easiest way is prime factorization: ( http://www.mathsisfun.com/prime-factorization.html) You would "prime factorize" the number inside the root to see if it is composed of any prime that has a power of 2 or more Ex. $98 = 2*7^2$ Since 7 is squared in the prime factorization, we can take the 7 out (because sqrt and ^2 cancel out. However, 2 doesn't cancel out and therefore stays inside the radical. Ex. 2 $\sqrt{343}$$343 = 7^3$ Since 7 is cubed, we can take out the 7, BUT NOT ALL OF IT. Only the 7^2 can come out (or a 7^4, or 7^6), and so the answer is $7\sqrt{7}$ Does that make more sense?

4. anonymous

I will check out the prime factorization website forthwith =) I have always had to use the guess and get discouraged method in the past.