Question

Simplify. Dividing radicals

Answer 1

Answer:

$\frac{\sqrt[4]{15} }{16}$

Step-by-step explanation:

You cannot leave a radical in the denominator, so the first step is to get rid of it. The way you do that is by multiplying the radical in the denominator by itself over itself because anything over itself is equal to 1. So, for example in this problem:

$\frac{\sqrt{15}}{\sqrt{16} } *\frac{\sqrt{16}}{\sqrt{16} }$

From here you multiply straight across. The numerator will be equal to $\sqrt{240}$ and the denominator will be 16 because any radical multiplied by itself cancels the radical out and just equals the number inside of the radical. The last step is to simplify the numerator. You do this by finding factors of 240 which are:

• 1 * 240
• 2 * 120
• 3 * 80
• 4 * 60
• 5 * 48
• 6 * 40
• 8 * 30
• 10 * 24
• 12 * 20
• 15 * 16

You want to use the greatest factor you have so you can break it down easier which in your case is (15 * 16). From here you simplify each of those numbers until you have a duplicate of something. The greatest factor of 15 is 3 * 5, so that won't simplify because there are no duplicate numbers. The greatest factor of 16 is 4 * 4 which means that it will simplify. When you are simplifying the duplicate (4) always goes outside of the radical and the non-duplicate (15) always goes on the inside of the radical. Your answer should look like this:

$\frac{\sqrt[4]{15} }{16}$