Question

NEED HELP ASAPPPPP      95 points? 4 problems! please help! Algebra..

1. Two passengers on a cruise ship look out across the horizon. One of the passengers who is standing on the upper deck can see a distance of √48 miles. The other passenger who is standing on the lower deck can see a distance of √27 miles.
Write an expression to represent the difference between the two distances each passenger can see. Then simplify the expression, keeping your answer in radical form. Show all steps needed to write your answer in simplest form.

2. A research scientist uses radar to track the migration of various types of birds. She estimates that a certain flock of geese traveled a distance of √750 on one day and
√1080 miles the next day.

Write an expression to represent the total distance covered by the geese over the two day period. Then simplify the expression, keeping your answer in radical form. Show all steps needed to write your answer in simplest form.

3. Before embarking on a flight, the pilot of a private airplane plans the best route to the final destination. Suppose the pilot determines one route covers a distance of √500 miles and another covers a distance of √605 miles.

Write an expression to represent the difference between the two distances of each route. Then simplify the expression, keeping your answer in radical form. Show all steps needed to write your answer in simplest form.

4. An engineer in a computer manufacturing company is trying to determine the best way to align two circuit boards in a new laptop computer. Suppose one of the circuit boards has a diagonal measurement of √24 centimeters and the other has a diagonal measurement of √54 centimeters.

Write an expression to represent the total length across the diagonals of both circuit boards. Then simplify the expression, keeping your answer in radical form. Show all steps needed to write your answer in simplest form.

Answer 1

1. We've got everything to write the expression. Here it is: √48 - √27.
We can simplify it into:
1) (√16 * 3) - (√9 * 3);
2) 4√3 - 3√3;
3) √3.

2. Here we also have everything to write the expression which represents the total distance covered by this over the two day period. The expression looks like this: √750) + √1080.We were asked to simplify that:
1) (√25 * 30) + (√36 * 30);2) 5√30 + 6√30;3) 11√30.

3. The same situation. We have all we need to write an expression to represent the difference between the two distances of each route. Here is the expression: √605 - √500.
We need to simplify it:1) (√121 * 5) - (√100 * 5);2) 11√5 - 10√5;
3) √5.

4. We've got all values to write the expression which represents the total length across the diagonals of both circuit boards. It looks like this: √24 + √54.
Then let's simplify it step by step1) (√4 * 6) + (√9 * 6);2) (2√6) + (3√6);3) 5√6.