Square Roots, Cube Roots and Estimating

Which expression is closest to the sum of the square root of 62 and the square root of 95?

• 7+9
• 7+10
• 8+9
• 8+10

When looking out over a large body of water, an observer can calculate the distance to the horizon by using the formula, d=√1.5h where d is the distance to the horizon (in miles), and h is the height above sea level of the observer’s eye (in feet). The height of the observer’s eye is 9 feet above sea level. Between which two values is the distance to the horizon?

• between 0 and 1 miles
• between 3 and 4 miles
• between 6 and 7 miles
• between 13 and 14 miles

A square room has an area of 150 square feet. Which of the following numbers is closest to the length of a side of the room?

• 12 ¹/₅ feet
• 12 ¹/₄ feet
• 12 ³/₁₀ feet
• 12 ¹/₂ feet

Which of the following is closest to the value of √11?

• 3
• 3.2
• 3.3
• 3.4

A cube has a volume of 800 cubic units. The length of the edge of this cube is between which two numbers?

• 9 and 10 units
• 11 and 12 units
• 20 and 21 units
• 28 and 29 units

Which number best approximates the value of x? (Click the question to see the answer choices)

• √6
• √7
• √46
• √52

The ∛24 is closest to which point on the number line?

• A
• B
• C
• D

A square tile has an area of 75 square inches. Which is the best estimate for the length of one side of the tile?

• between 6 and 8 inches
• between 8 and 10 inches
• between 37 and 50 inches
• between 64 and 81 inches

The √136 is between which two numbers?

• 9 and 10
• 10 and 11
• 11 and 12
• 12 and 13

Given that the square root of 225 is 15 and the square root of 256 is 16, which number is closest to the square root of 240?

• 15.1
• 15.5
• 158
• 15.9