Estimating Square Roots

Jennifer is purchasing a square canvas for a custom artwork piece she will create. She wants the canvas to have a side length that is between 8 and 9 inches. She finds a canvas with the area shown at the right (Area = 90 in²). What is the estimated side length of the canvas?

• 9.5 inches

• 8.5 inches

• 7.5 inches

• 10 inches

Did this canvas meets Jennifer’s requirements?

(She wanted the canvas to have a side length that was between 8 and 9 inches.)

• Yes, the canvas meets Jennifer’s requirements.

• No, the canvas does not meet Jennifer’s requirements.

• The canvas partially meets Jennifer’s requirements.

• The canvas exceeds Jennifer’s requirements.

The area of the canvas shown represents a __________ square. We can use our knowledge of perfect squares to estimate the square roots of non-perfect squares.

• non-perfect

• perfect

• prime

• even

PERFECT SQUARES • Numbers whose square roots are __________. • Examples: _____ _____ _____

• whole numbers; 1, 4, 9

• fractions; 2, 3, 5

• decimals; 2.5, 6.7, 8.1

• prime numbers; 2, 3, 5

NON-PERFECT SQUARES • Numbers whose square roots are not __________. • Examples: _____ _____ _____

• whole numbers; 2, 3, 5

• even numbers; 4, 6, 8

• prime numbers; 7, 11, 13

• fractions; 1/2, 3/4, 5/6

Estimate the value of √50. Use the number line to locate the whole numbers that √50 should be between.

• √50 is between 7 and 8.

• √50 is between 6 and 7.

• √50 is between 8 and 9.

• √50 is between 5 and 6.

Estimate the value of √50. Which whole number is √50 closer to?

• 7

• 8

• 6

• 9

Estimate the value of √50. Estimate √50 to the nearest tenth.

• √50 ≈ 7.1

• √50 ≈ 6.2

• √50 ≈ 8.0

• √50 ≈ 7.8

Estimate the value of √22. √22 is between _____ and _____, but closer to _____. Decimal estimate: √22 ≈ _____.

• √22 is between 4 and 5, but closer to 5. Decimal estimate: √22 ≈ 4.7.

• √22 is between 3 and 4, but closer to 4. Decimal estimate: √22 ≈ 3.9.

• √22 is between 5 and 6, but closer to 6. Decimal estimate: √22 ≈ 5.8.

• √22 is between 2 and 3, but closer to 3. Decimal estimate: √22 ≈ 2.9.

Estimate the value of √103. √103 is between _____ and _____, but closer to _____. Decimal estimate: √103 ≈ _____.

• √103 is between 10 and 11, but closer to 10. Decimal estimate: √103 ≈ 10.1.

• √103 is between 9 and 10, but closer to 10. Decimal estimate: √103 ≈ 9.9.

• √103 is between 11 and 12, but closer to 11. Decimal estimate: √103 ≈ 11.2.

• √103 is between 10 and 11, but closer to 11. Decimal estimate: √103 ≈ 10.9.