Unit 1 Worksheet 5 Square and Square Roots class- 8 DAV Secondary Mathematics Solutions

Q5. Estimate the value of the following to the nearest one decimal place.
(i) 90 (ii) 150 (iii) 600 (iv) 1000
Sol. (i) The perfect square near 90 are 81 and 100.
∴ 81 < 90 < 100 ⇒ 9² < 90 < 10² So we can estimate the value between 9 and 10. Let us try with 9.5. ∴ 9.5 × 9.5 = 90.25 > 90
∴ 9² < 90 < 9.5² Now 9.4 × 9.4 = 88.36 < 90 Hence, the estimated value of √90 is 9.48.

(ii) The perfect square number near 150 are 144 and 169. ∴ 144 < 150 < 169 ⇒ 122 < 150 < 132 So we can estimate the value of 150 between 12 and 13. Let us try for 12.5. ∴ 12.5 × 12.5 = 156.25 > 150 ∴ 12² < 150 < 12.5² and 12.4 < 12.4 = 153.76

∴ 12² < 150 < 12.4² 12.3 × 12.3 = 151.29 > 150

∴ 12² < 150 < 151.29 12.2 × 12.2 = 148.84 < 150 ∴ 148.84 < 150 < 151.29

∴ 12.2² < 150 < 12.4² ∴ Estimated value of √150 = 12.25.

(iii) The perfect squares near 600 are 576 and 625. ∴ 576 < 600 < 625 ⇒ 24² < 600 < 25² Let us try for 24.5. ∴ 24.5 × 24.5 = 600.25 > 600
∴ 24² < 600 < 24.5²

24.495² = 600.005 Hence, the estimated value of √600 = 24.495

(iv) The perfect square numbers near 1000 are 961 and 1024. ∴ 961 < 1000 < 1024 ⇒ 31² < 1000 < 32² Let us try for 31.5 ∴ 31.5 × 31.5 = 992.25 < 1000 and 31.6 × 31.6 = 998.56 < 1000 then 31.7 × 31.7 = 1004.89 > 1000
∴ 31.6² < 1000 < 31.7²
31.62² = 999.82 < 1000
Hence, the estimated value of √1000 is 31.63.

Q6. Devika has a square piece of cloth of area 9 m2 and she wants to make 16 square-shaped scarves of equal size out of it. What should possibly be the length of the side of the scarf that can be made out of this piece?
Sol. Area of 1 square shaped scarf = 9/16 m2

Q7. The area of a square plot is 800 m2. Find the estimated length of the side of the plot.
Sol. The perfect square numbers near to 800 are 784 and 841.
∴ 784 < 800 < 841 ⇒ 28² < 800 < 29²
Let us check for 28.5.

∴ 28.5 × 28.5 = 812.25 > 800
∴ 28² < 800 < 28.5²
28.4 × 28.4 = 806.56 < 800
∴ 28² < 800 < 28.4
28.3 × 28.3 = 800.89
∴ 28² < 800 < (28.3)²
28.2 × 28.2 = 79.524 < 800
∴ 28.2² < 800 < 28.3²
∴ Estimated value of 800 = 28.25
Hence, the length of the side of the plate = 28.25 m