Introduction to Radicals

Show your work for each problem.

1.
What is ?
1. a)2
2. b)32
3. c)4
4. d)8
Answer: 4
because . Remember: the square root is NOT division by 2.
2.
Calculate
Answer: 5
because .
3.
In the expression , what is the radicand?
1. a)7
2. b)49
3. c)The square root symbol
4. d)2
Answer: 49
The radicand is 49 - it's the number under the radical sign. The answer 7 is the result of taking the square root.
4.
Find the value of
Answer: 9
1. What does the square root ask us to find? a number that when multiplied by itself gives 81
2. What is ? 81
3. So what is ? 9
5.
What is ?
Answer: 10
because .
6.
Which of the following is NOT a perfect square?
1. a)50
2. b)49
3. c)64
4. d)36
Answer: 50
50 is NOT a perfect square. , , , but 50 is between and - no whole number squares to 50.
7.
If , find the value of .
Answer: 36
1. To undo a square root, what operation do we use? squaring
2. Square both sides: . What is ? 36
3. So 36
8.
Calculate
Answer: 12
because .
9.
Between which two consecutive integers does lie?
Answer: 5 and 6
1. What is ? 25
2. What is ? 36
3. Is 30 between 25 and 36? yes
4. So is between which two integers? 5 and 6
10.
What is the value of ?
1. a)12
2. b)3 + 4 = 7
3. c)5
4. d)25
Answer: 5
. Note: . You cannot split a square root over addition!
11.
If , what is the positive value of ?
Answer: 11
If , then . The positive value is .
12.
A square has an area of 196 square centimeters. What is the length of one side?
Answer: 14
1. The area of a square is side × side = side². If area = 196, what equation do we have? side² = 196
2. To find the side, we need to take the square root. What is ? 14
3. So the side length is ___ cm 14
13.
What is the value of ?
1. a)25
2. b)5
3. c)-25
4. d)-5
Answer: 5
, then . The square root always gives a non-negative result: .
14.
A right triangle has legs of length 6 and 8. Find the length of the hypotenuse using the Pythagorean theorem.
Answer: 10
1. The Pythagorean theorem says . What is ? 36
2. What is ? 64
3. What is ? 100
4. What is ? 10
15.
If , what is the value of ?
Answer: 144
If , then . We can verify: . Correct!
16.
A rectangular field is 80 meters long and 60 meters wide. What is the length of the diagonal path across the field?
Answer: 100
1. The diagonal forms a right triangle. Using Pythagorean theorem: . What is ? 6400
2. What is ? 3600
3. What is ? 10000
4. What is ? 100