Simplify each radical?

Question

a) square root of 3 plus the square root of 27

b) square root of 98 subtract the square root of 32

c) 72 divided by 3

Answer 1

I will use v/ = Square Root symbol

v/ 3 + v/ 27 = v/ 3 + (3 * v/ 3) = 4 v/ 3
= 4 times square root of 3
[see note below]

v/ 98 - v/ 32 = (7 * v/ 2) - (4 * v/ 2) = 3 v/ 2
= 3 times square root of 2
[see note below]

72 / 3 = 24
Are you sure there are no v/ radicals in this problem?

Notes: v/ 27 = v/ (9 x 3) = ( v/ 9)( v/ 3) = (3 * v/ 3)

To check that v/ 27 = (3 * v/ 3)
take the original expression, square it (multiply times itself)
take the final expression, square it (multiply times itself)
You should get the same answer, if not something is wrong

Check: v/ 27 times itself = 27
3 * v/ 3 times itself = (9 x 3) = 27
So these are the same value, v/ 27 = (3 * v/ 3)

For v/ 98 = v/ (49 x 2) = ( v/ 49) x ( v/ 2) = 7 * v/ 2
For v/ 32 = v/ (16 x 2) = ( v/ 16 ) x ( v/ 2) = 4 * v/ 2
Always look for a number that is a perfect square,
then you can separate that part and reduce it outside the radical
v/ 49 --> 7
v/ 16 --> 4

Answer 2

a) 6.92820323
b) -4.242640687
c) 24