Roots and Radicals

​Roots and Radicals

​What number times itself equals the number under the radical symbol.

Square roots

​Square roots

​Square roots are the INVERSE of squaring a number.

​Square roots

​Perfect Squares

​Always a good idea to have these memorized

​When the answer to the square root is a whole number.

Multiple Choice

√100

• 15

• 10

• 11

• 12

Multiple Choice

What is the square root of 49?

• 7

• 8

• 6

• 5

Multiple Choice

What is $$-\sqrt[]{225}$$

• 15

• -15

• $$\pm$$ 15

• not possible

​NON-perfect squares

​Any number whose square root is NOT a whole number. (has a decimal)

​Approximating Square Roots

​You can approximate the square of a non-perfect square by finding what two perfect squares the number falls between.

Multiple Choice

The √20 is between which two integers?

• 2 & 3

• 3 & 4

• 4 & 5

• 5 & 6

Multiple Choice

The √40 is between which two integers?

• 7 & 8

• 6 & 7

• 5 & 6

• 4 & 5

Multiple Choice

The $$\sqrt[]{23}$$ is closest to which perfect square?

• 4

• 5

• 6

• 7

Multiple Choice

The $$-\sqrt[]{122}$$ is closest to which perfect square

• 10

• -10

• 11

• -11

Rules of Square roots

• Every positive number has both a positive and a negative square root.

• ​A negative number has no real square root

  • NO number times ITSELF will equal a negative

Match

Match the following

• $$\sqrt[]{4}$$

• $$\sqrt[]{9}$$

• $$\sqrt[]{16}$$

• $$\sqrt[]{25}$$

• $$\sqrt[]{36}$$

• $$\pm2$$

• $$\pm3$$

• $$\pm4$$

• $$\pm5$$

• $$\pm6$$

Multiple Choice

The area of the square piece of paper is 324 sq inches. How long is one side of the paper.

Formula for the area of a square is

$$a=s^2$$

• 17 inches

• 18 inches

• 19 inches

• 16 inches

Multiple Choice

The height of the observation window in the tower of the castle is 121 feet off the ground. How far can the guard see on a clear day? Use the formula $$d=1.22\cdot\sqrt[]{h}$$ where d is the distance to the horizon in miles and h is the height of the observer.

• 13.42 miles

• 147.62 miles

• 12.15 miles

  (to nearest hundredth)

• 99.18 miles

  (to nearest hundredth)

Cubed root means what number times itself times itself equals the number under the radical sign

​

​Cubed roots

​Perfect Cube roots

​When the cubed root of a number equals a whole number

​Good idea to know at least 1-5

Multiple Choice

• 9

• 3

• 1/3

• 1

Multiple Choice

What is the cube root of 125?

• 5

• -5

• 25

• -25

Multiple Choice

∛1

• 1

• 3

• 4

• 2

Rules of Cubed roots

• All positive numbers will have a positive cubed root.

• ​All negative numbers have a negative cubed root

​=

Multiple Choice

∛-8

• 2

• -2

• 4

• -4

Multiple Choice

Find the cube root. 

• -4

• 4

• 8

• -8

Multiple Select

Select all perfect cubes

• 2

• 8

• 27

• 64

• 9