Worksheet: Approximating Radicals

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 √ 8 3 to the nearest whole number.

Q2:

The radius π‘Ÿ of a sphere is given by the formula π‘Ÿ = ο€Ό 3 𝑉 4 πœ‹    , where 𝑉 is the sphere’s volume. Determine the difference in radius between a sphere with volume 7 , 7 7 6 πœ‹ and a sphere with volume 1 8 , 4 3 2 πœ‹ .

Q3:

Which of the integers below is the closest to  √ βˆ’ 3 5 3 ?

  • A βˆ’ 6
  • B βˆ’ 1 8
  • C βˆ’ 1 7
  • D βˆ’ 7

Q4:

What is the value of 1 6 √ 5 + 1 8  ? Give your answer to the nearest tenth.

Q5:

Find the two consecutive one-decimal-place numbers that  √ 7 3 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 π‘₯ which satisfies the following equation π‘₯ < √ βˆ’ 5 7 < π‘₯ + 1  .

Q7:

If π‘₯ ∈ β„€  , and π‘₯ <  √ 5 1 3 < π‘₯ + 1 , find the value of π‘₯ .

  • 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 π‘Ÿ of a certain circle is given by π‘Ÿ = √ 3 8 , estimate the radius of the circle to the nearest foot.

Q11:

Estimate  √ 7 9 to the nearest whole number.

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