One thing I learned in the second week of math 10 is how to simplify entire radicals.

  • First you need to find the radical you would like to simplify, lets use \sqrt{45}.
  • Next you need to find the prime factorization of it, so in our case it would be \sqrt{3\cdot 3\cdot 5}.
  • Now you find the pairs, the numbers with pairs will leave the square root symbol, and the rest will not.  3 \sqrt{5}
  • Next you need to clean everything up if there are remaining multiples, multiply the coefficients and the numbers inside the square root if needed. In our example we do not need to multiply anything.

In pair with this, I also learned how to convert mixed radicals into entire radicals.

  • Firstly you still have to find the mixed radical you would like to convert. For this example we will use 2 \sqrt[3]{18}
  • Next you have to put the coefficient back into the square root sign, for example: since this one is a cubed root you need to multiply the 2 into the square root 3 times. \sqrt {2\cdot 2\cdot 2\cdot 18}
  • Now you do some simple multiplying (multiply all the number inside the square root sign together)
  • Which will give you the answer: \sqrt {144} which happens to equal 12