1. You need to multiply the denominator by something that will make the content of the radical be a square—so that when you take the square root, you get something rational. Easiest and best is to multiply by √6. Of course, you must multiply the numerator by the same thing. Then simplify.
![\displaystyle\frac{2}{\sqrt{6}}=\frac{2}{\sqrt{6}}\cdot\frac{\sqrt{6}}{\sqrt{6}}\\\\=\frac{2\sqrt{6}}{\sqrt{6}\cdot\sqrt{6}}=\frac{2\sqrt{6}}{6}\\\\=\bf{\frac{\sqrt{6}}{3}}](https://tex.z-dn.net/?f=%5Cdisplaystyle%5Cfrac%7B2%7D%7B%5Csqrt%7B6%7D%7D%3D%5Cfrac%7B2%7D%7B%5Csqrt%7B6%7D%7D%5Ccdot%5Cfrac%7B%5Csqrt%7B6%7D%7D%7B%5Csqrt%7B6%7D%7D%5C%5C%5C%5C%3D%5Cfrac%7B2%5Csqrt%7B6%7D%7D%7B%5Csqrt%7B6%7D%5Ccdot%5Csqrt%7B6%7D%7D%3D%5Cfrac%7B2%5Csqrt%7B6%7D%7D%7B6%7D%5C%5C%5C%5C%3D%5Cbf%7B%5Cfrac%7B%5Csqrt%7B6%7D%7D%7B3%7D%7D)
2. Identify the squares under the radical and remove them.
![5\sqrt{12xm^3}=5\sqrt{(4m^2)(3xm)}=5\sqrt{(2m)^2}\sqrt{3xm}\\\\=5\cdot 2m\sqrt{3xm}=\bf{10m\sqrt{3xm}}](https://tex.z-dn.net/?f=5%5Csqrt%7B12xm%5E3%7D%3D5%5Csqrt%7B%284m%5E2%29%283xm%29%7D%3D5%5Csqrt%7B%282m%29%5E2%7D%5Csqrt%7B3xm%7D%5C%5C%5C%5C%3D5%5Ccdot%202m%5Csqrt%7B3xm%7D%3D%5Cbf%7B10m%5Csqrt%7B3xm%7D%7D)
Answer:
![\frac{6}{11}](https://tex.z-dn.net/?f=%5Cfrac%7B6%7D%7B11%7D)
Step-by-step explanation:
we know that
To find what fraction of the remaining pieces are apple, divide the remaining pieces of apple by the total remaining pieces
we have that
the remaining pieces of apple is equal to 6
the total remaining pieces is 11
so
![\frac{6}{11}](https://tex.z-dn.net/?f=%5Cfrac%7B6%7D%7B11%7D)