now let's talk about square roots what is the square root of 25 what number times itself is 25 5 times 5 is 25 so the square root of 25 is 5. now what about negative square root 25 and the square root of negative 25 what's the answer for these well we know the square root of 25 is 5 and there's a negative in front so it's negative 5. and if you have a negative on the inside just keep in mind that the square root of negative 1 is the imaginar the imaginary number i so this is going to be 5i try these three the square root of 81 negative root 81 and also the square root of negative 81. so this is equal to positive nine this is equal to negative nine and this is going to be 9i what is the square root of 36 divided by 49 and also negative root 121 over 169 go ahead and try these two the square root of 36 is 6 and the square root of 49 is 7. that's all you need to do for this one the square root of 121 is 11 and the square root of 169 is 13. and what about this one negative 81 over 144 go ahead and simplify that example the square root of 81 is 9 the square root of 144 is 12. and because we have a negative sign on the inside we need to include the imaginary number i now we can reduce nine over twelve nine is basically three times four i mean not three times four three times three twelve is three times four so we can cancel a three so therefore the answer is three over four times i now what is the square root of point 16 what do you think the answer is notice that there's two digits to the right of the decimal point and when you take the square root the answer should only contain one digit to the right of the decimal point the square root of 16 is four so it's going to be 0.4 since it has one digit to the right what about the square root of point zero zero two five notice that there's four digits to the right of the decimal and four divided by two is two so the final answer should have two digits to the right of the decimal point the square root of 25 is five so this is going to be .05 as you can see it has two digits to the right of the decimal point and now what about this one the square root of point zero zero zero zero eight one notice that we have six digits to the right of the decimal point six divided by two is three so the final answer should have three digits to the right of the decimal point the square root of eighty one is nine so this is going to be point zero zero nine now let's talk about cube roots what is the cube root of eight what number times itself three times is eight two times two times two is eight which is basically two to the third so therefore the cube root of eight is two now what is the cube root of negative twenty-seven this it turns out it's negative three negative three multiplied to itself three times is negative 27 and how about the cube root of 64 but with a negative on the outside the cube root of 64 is 4. negative 4 multiplied to itself three times is negative 64. now what is the cube root of 125 over 216 the cube root of 125 is 5 because 5 to the third is 125 and the cube root of 2 16 is 6 because if you multiply 6 3 times you're going to get 216. now what is the cube root of a decimal let's say .008 notice that we have three digits to the right of the decimal point take that number and divide it by the index number your final answer should have one digit to the right of the decimal point now we know that the cube root of 8 is 2. so this is just going to be 0.2 as you can see it has one digit to the right of the decimal point now what is the cube root of zero zero zero two seven notice that it has six digits to the right of the decimal point six divided by the index number three is two so our final answer should have a total of two digits to the right of the decimal point the cube root of 27 is three so the final answer is point zero three with two digits let's try one more example like that what is the cube root of point zero zero zero zero zero zero zero six four so we have a total of nine digits the cube root of 64 is four and nine divided by three is three so our final answer should have three digits to the right of the decimal point so it's point zero zero four and so that's how you can take the square root or cube root of decimal numbers if the number of digits is a multiple of the index number you