What if the last term has a square root that is a big, long decimal? you wouldn't use the decimal, would you?
you would round it off to the hundreds place or put it as a fraction.. whatever your teacher wants you to do....but you do need the numbers after the decimal point
You would usually simplify the square root as much as possible, say... 4 square root of 80. Nothing times it's self is 80, but it does have factors you can work with. 8 and 10 are easy... 8 has a factor of 4 and 2. 4 can be simplified down into 2 and 2. One of those goes away, and one goes to the outside. The ten can factor into 5 and 2. You have two two's and a five inside the square root. Another goes away and another goes to the outside. you are left with 2, 4, and 2 on the outside. You multiply them and have 16 square root of 5, because the five is still inside the square root...That was extremely long winded, but I hope it helps...
When dealing with expressions or equations, it is generally preferred to leave the terms in their simplest form. This means that if the last term of an expression has a square root that is a big, long decimal, it is typically not advisable to use the decimal approximation.
Instead, it is recommended to keep the square root in the simplest radical form. This means leaving the expression in terms of the square root symbol (√) without any decimal or decimal approximation.
For example, let's say we have the expression: √3 + 2√5 + √7 + √10. If the value of √10 is approximately 3.162, it would be preferred to leave the expression as √3 + 2√5 + √7 + √10 rather than replacing √10 with its decimal approximation.
Keeping the expression in radical form ensures accuracy and allows for further simplifications or calculations to be performed, if necessary, without losing precision due to rounding errors.
Remember, in mathematics, it is generally preferred to work with exact values whenever possible, rather than approximations.