Radical Word Problems

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1.
A ladder is 2.5 meters long. Its top reaches 2.4 meters up a wall. How far is the foot of the ladder from the wall?
1. a)3.47 m
2. b)0.1 m
3. c)0.7 m
4. d)0.49 m
2.
A square garden has an area of 144 square meters. What is the side length?
3.
What formula would you use to find the diagonal of a rectangle with length 8 and width 6?
1. a) $d = \sqrt{8 \times 6}$
2. b) $d = 8 \times 6$
3. c) $d = \sqrt{8^2 + 6^2}$
4. d) $d = 8 + 6$
4.
A rectangular TV screen is 32 inches wide and 24 inches tall. Find the diagonal (screen size).
5.
Find the distance between points $(0, 0)$ and $(3, 4)$ .
6.
A square has an area of 72 square cm. What is the side length in simplest radical form?
1. a) $9\sqrt{2}$ cm
2. b) $6\sqrt{2}$ cm
3. c) $\sqrt{72}$ cm
4. d) $2\sqrt{18}$ cm
7.
Find the distance between points $A(2, 3)$ and $B(8, 11)$ .
8.
A kite string is 25 meters long. The kite is directly above a point 7 meters from the person holding the string. How high is the kite?
9.
A town square has the shape of a square with 90-meter sides. A straight path crosses it from one corner to the opposite corner. How long is the path? Give the answer in simplest radical form.
10.
The sloping side of a barn roof rises 5 meters over a horizontal distance of 12 meters. How long is the sloping roof edge?
1. a)15 m
2. b)13 m
3. c)17 m
4. d) $\sqrt{119}$ m
11.
A rectangular pool is 15 meters by 8 meters. A swimmer swims diagonally across. What is the exact distance?
12.
Find the distance between $(1, 5)$ and $(4, 11)$ . In simplest radical form it is $a\sqrt{5}$ . What is $a$ ?
13.
A 20-meter cable runs from the top of a mast to a stake in the ground. The stake is 16 meters from the foot of the mast. How tall is the mast?
14.
Find the distance between $(-2, 3)$ and $(1, -1)$ .
1. a) $\sqrt{7}$
2. b) $\sqrt{5}$
3. c)7
4. d)5
15.
A helicopter hovers at a height $h$ . A straight rescue line, 130 meters long, is stretched from the helicopter to a boat on the water. The boat is 50 meters from the point directly below the helicopter. How high is the helicopter?
16.
A square has a diagonal of $10\sqrt{2}$ cm. What is the side length?