SIMPLEST RADICAL FORM WORKSHEET

Problem 1 :

What is √45 in simplest form?

a. 5√3     b. 9√5     c. 3√5     d. 15√3

Solution

Problem 2 :

What is √90x⁵ y⁴ in simplest radical form?

a. 10x²y² √9x       b. 9x³y² √10x²y²

c. 3x²y² √10x        d. 18x⁴y³ √5xy

Solution

Problem 3 :

Which radical expression when expressed in simplified form is 3√13?

a. √16     b. √39      c. √117      d. √507

Solution

Problem 4 :

Which value could replace the? to make the expression true?

√12a⁶b³ = 2a³b√?

a. 6b²       b. 3b      c. 4a³b²     d. 3a²b

Solution

Problem 5 :

For what value of x does ∛x simplify to 4∛5?

a. 20     b. 80      c. 320     d. 460

Solution

Problem 6 :

If y³ = -56, what is the value of y?

a. -2∛14    b. -8∛7     c. -2∛7     d. -7∛8

Solution

Problem 7 :

Write the radical expression ∛-216 in simplest form.

Solution

Problem 8 :

Which value could replace the? To make expression true?

∛486 = 3∛?

Solution

Problem 9 :

∛24 - 7√3

Solution

Problem 10 :

8√2 + 3√8

Solution

Problem 11 :

(-5√36) (3√2)

Solution

Problem 12 :

(3a²√3) (a√12)

a. 3a³√15    b. 18a³    c. 4a⁴√12    d. 9a³√2

Solution

Problem 13 :

The distance d (in miles) that you can see to the horizon with your eye level h feet above the water is given by

d = √(3h/2)

How far can you see when your eye level is 5 feet above the water?

Solution

Problem 14 :

Evaluate the function for the given value of x.

a) h(x) = √5x, x = 10

b) g(x) = √3x, x = 60

c) r(x) = √[3x/3x² + 6)], x = 4

Solution

Problem 15 :

What are the perimeter and area of a rectangle with length of 5√3 centimeters and width of 3√2 centimeters?

Solution

Problem 16 :

What are the perimeter and area of a rectangle with length of 2√6 centimeters and width of √3 centimeters?

Solution

Problem 17 :

If the base of a triangle measures 6√2 meters and the height measures 3√2 meters, then what is the area?

Solution

Expand and simplify :

Problem 1 :

(1 + √2) (2 + √2)

Solution

Problem 2 :

(2 + √3) (2 + √3)

Solution

Problem 3 :

(√3 + 2) (√3 - 1)

Solution

Problem 4  :

(4 - √2) (3 + √2)

Solution

Problem 5 :

(1 + √3) (1 - √3)

Solution

Problem 6 :

(5 + √7) (2 - √7)

Solution

Problem 7 :

(√5 + 2) (√5 - 3)

Solution

Problem 8 :

(√7 - √3) (√7 + √3)

Solution

Problem 9 :

(2√2 + √3) (2√2 - √3)

Solution

Problem 10 :

(4 - √2) (3 - √2)

Solution

Problem 11 :

Find the integer part of the sum (√2 + √3)⁴

Solution

Problem 12 :

Solve for x in the following equation 2√(x² + 1) = 9

Solution

Problem 13 :

Simplify the following 

(³√x⁷) (⁵√x⁵)

Solution

Problem 14 :

Solve the equation 

2^x+2 = 4√2

Solution

Problem 15 :

If √4x + √9x² = 3, find the value of x.

Solution

Expand and simplify :

Problem 1 :

(4 + √3) (4 - √3)

Solution

Problem 2 :

(5 - √2) (5 + √2)

Solution

Problem 3 :

(√5 - 2 ) (√5 + 2)

Solution

Problem 4 :

(√7 + 4 ) (√7 - 4)

Solution

Problem 5 :

(3√2 + 2 ) (3√2 - 2)

Solution

Problem 6 :

(2√5 - 1 ) (2√5 + 1)

Solution

Problem 7 :

(5 - 3√3) (5 + 3√3)

Solution

Problem 8 :

(2 - 4√2) (2 + 4√2)

Solution

Problem 9 :

(1 + 5√7) (1 - 5√7)

Solution

Problem 10 :

Find the area of the rectangle shown in the figure

Solution

Problem 11 :

Find the area of the rectangle shown in the figure

Solution

Problem 12 :

Complete the statement √2 √5 = √10 because

Solution

Problem 13 :

Complete the statement 2√3 + 5√3 = 7√3 but 7√3 + 3√5 ≠ 10√8

Solution

Problem 14 :

The radius r of a sphere is given by

r = ³ √(3/4π) V

where V is the volume of the sphere. Estimate the volume of a spherical head of brain coral with a radius of 1.5 feet.

Solution

Problem 15 :

The mean sustained wind velocity (in meters per second) of a hurricane is modeled by

v( p) = 6.3 √(1013 − p)

where p is the air pressure (in millibars) at the center of the hurricane. Estimate the air pressure at the center of the hurricane when the mean sustained wind velocity is 54.5 meters per second.

Solution