S OLVING FOR R ADIUS AND D IAMETER

W HAT IF WE WANTED TO FIND THE RADIUS AND DIAMETER OF A CIRCLE GIVEN THE AREA ? Use π = 3.14 to find the radius of this circle. A = πr² A = 100 cm How can we rearrange this to make the radius the subject of the formula? ? r² = A π How can we undo r² ? We need to learn how to take the square root of a number.

Think about the relationship between the area of a square and the length of one of its sides. Taking the square root of a number is the inverse operation of squaring the number. Every positive number has two square roots, one positive and one negative. One square root of 36 is 6, since 6 6 = 36. The other square root of 36 is –6, since (–6) (–6) is also 36. You can write the square root of 36 as ±6, meaning “plus or minus” 6. area = 36 square units side length = 6 2 = 36 R ELATIONSHIPS AND D EFINITIONS 6 units 36 = 6

P ERFECT S QUARES These are perfect squares. They have the same length and the same width. Area = length ∙ width

What are the square roots of 81? 9 2 = 81 and (-9) 2 = 81. The square roots of 81 are 9 and -9. We can write it as ± 9. What are the square roots of 49? F INDING S QUARE R OOTS ± 7

Sometimes, when you find the square roots of a number, the square roots will NOT be WHOLE NUMBERS. This is why you NEED your calculator. Use the square root button to find the square roots. If you get a decimal number, round to the nearest hundredth. W HEN YOU DON ’ T HAVE PERFECT SQUARES …

What are the square roots of 78? What are the square roots of 173? Y OU T RY ! 8.83 and (±8.83) and (±13.15)

13 2 = 169 The window is 13 inches wide. Find the square root of 169 to find the width of the window. Use the positive square root; a negative length has no meaning. A square window has an area of 169 square inches. How wide is the window? So 169 = 13. E XAMPLE The area of a square is s 2, where s is the length of a side. Remember!

The table will fit through the door. Find the square root of 16 to find the width of the table. Use the positive square root; a negative length has no meaning. A square shaped kitchen table has an area of 16 square feet. Will it fit through a van door that has a 5 foot wide opening? So the table is 4 feet wide, which is less than 5 feet. 16 = 4 E XAMPLE

When we are finding the square root of r² we are looking for the radius. We learned that taking the square root of a positive number gives us two square roots. One negative and one positive. Can a radius of a circle be negative? Using Square Roots to Solve for Radius No. Because a radius is a distance. Distance is always measured in positive numbers. r

W HAT IF WE WANTED TO FIND THE RADIUS AND DIAMETER OF A CIRCLE GIVEN THE AREA ? Use π = 3.14 to find the radius of this circle. A = πr² A = 100 cm How can we rearrange this to make the radius the subject of the formula? ? r² = A π r = r = 5.64 cm Always round your answer to the nearest hundredth. We can also find the diameter since d = 2r d = cm

A TABLECLOTH FOR A ROUND TABLE HAS AN AREA OF 1,386 IN ². W HAT IS THE APPROXIMATE RADIUS OF THE TABLECLOTH ? Area = πr 2 1,386 = (3.14)r 2 r = in Example r =

F IND THE R ADIUS Find the diameter of a circle that has an area of square yards. Use 3.14 for.

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