Roots and Radicals

Vocabulary

100

What is a Pythagorean theorem?

In right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

a^2 +b^2 = c^2

200

What is a radical sign?

√

300

What is hypotenuse?

The longest side of the right triangle.

400

What is radicand?

The expression under the radical sign.

500

What is square root?

The square root of a number is a value that, when multiplied by itself, gives the number. 

Example: 4 × 4 = 16, so a square root of 16 is 4. 

Evaluate

100

- √196

- 14

200

∜(-5)^4

5

300

sixth root of√y^18

|y^3|

400

-81^1/4

-3

500

(-36)^3/2

Not a real number 

Simplify Radicals

100

√300

10√3

200

∜243

3 ∜3

300

√72y^3x

6y√2yx

400

- ∜(32a^5 b^7 )

- 2ab ∜(2ab^3 )

Application

100

In the right angle triangle, find the length of the unknown side. 

a = 14, b= 8, c = ?

2 √65

200

In right angle triangle, find the length of the unknown side.

a = 4, c = 6, b = ?

2√5

300

Find the equation of the circle with center at (2, -1) and radius √10

(x - 2)^2 + (y +1)^2 = 10

400

Find the distance between the pair of points (-3,2) and (0, -4)

3√5