In this worksheet, we will practice using a calculator to approximate the nth root of a number and then using it to solve real-world problems.

Q1:

By considering square numbers, determine an approximation for to the nearest whole number.

Q2:

The radius of a sphere is given by the formula , where is the sphereβs volume. Determine the difference in radius between a sphere with volume and a sphere with volume .

Q3:

Which of the integers below is the closest to ?

• A
• B
• C
• D

Q4:

What is the value of ? Give your answer to the nearest tenth.

Q5:

Find the two consecutive one-decimal-place numbers that lies between.

• A4.2, 4.3
• B4.0, 4.1
• C4.3, 4.4
• D4.1, 4.2
• E3.9, 4.0

Q6:

Find the integer which satisfies the following equation .

Q7:

If , and , find the value of .

• A9
• B7
• C8

Q8:

Given that a whole number is squared and that the result is between 875 and 974, determine between which of the following is the whole number.

• A33 and 35
• B31 and 33
• C27 and 29
• D29 and 31
• E25 and 27

Q9:

Nabil wants to buy fencing to enclose a square garden with an area of 380 ft2. How much fencing does he need to buy? Round your answer to the nearest tenth.

Q10:

Given that the radius of a certain circle is given by , estimate the radius of the circle to the nearest foot.

Q11:

Estimate to the nearest whole number.