1.04 Estimating square roots
State the integer that each of the following numbers is closet in value to:
Plot the following square roots on a number line:
Write a square root that has a value between 5 and 6.
Which one of the following has a value between 10 and 11?
Consider the number \sqrt{22}.
Complete the inequality with two consecutive perfect square numbers that 22 lies between:
⬚ < 22 < ⬚
Complete the inequality with two consecutive integers that \sqrt{22} lies between:
⬚ < \sqrt{22} < ⬚
Consider the number \sqrt{59}.
Complete the inequality with two consecutive perfect square numbers that 59 lies between:
⬚ < 59 < ⬚
Complete the inequality with two consecutive integers that \sqrt{59} lies between:
⬚ < \sqrt{59} < ⬚Determine the two consecutive integers that will complete the following inequalities:
State the integer that lies between \sqrt{12} and \sqrt{22}.
For each of the following pairs of numbers, select the number with the larger value:
\sqrt{27} or \sqrt{22}
\sqrt{50} or \sqrt{46}
\sqrt{20} or 5
\sqrt{15} or 3
For each of the following pairs of numbers, select the number with the smaller value:
4 \pi or 12
\pi^2 or 144
\sqrt{120} or 11
\sqrt{72} or 8
For the following roots:
Evaluate, correct to two decimal places where necessary.
State whether the solution is an exact value or an approximation.
Bob has a square-shaped pool with an area of 59\text{ m}^{2}. What is the approximate length of each side of his pool to the nearest meter?
Sophia wants to create a square photo frame that has an area of 24\text{ in}^{2}.
What is the approximate length of each side of the photo frame to the nearest inch?
Find the approximate length of the material (to the nearest inch) she would need to create the frame.