Model 2 Simplification based on square & square root Practice Questions Answers Test with Solutions & More Shortcuts

Answer: (d)

$√{{20.2 × 4}/{0.25 × 20.2}} = √{4/{0.25}}$

= $√{400/25} = √{16}$ = 4

Answer: (c)

? = ${(3.4567 + 3.4533)(3.4567 - 3.4533)}/{0.0034}$

= ${6.9100 × 0.0034}/{0.0034}$ = 6.91

Using Rule 8,

${(3.4567 + 3.4533)(3.4567 - 3.4533)}/{0.0034}$

= ${{3.4567}^2 - {3.4533}^2}/{(3.4567 - 3.4533)}$

= 3.4567 + 3.4533 = 6.91

Answer: (a)

Expression

= $√{{0.009 × 0.036 × 0.016 × 0.08}/{0.002 × 0.0008 × 0.0002}}$

= $√{{9 × 36 × 16 × 8}/{2 × 8 × 2}}$

= 3 × 2 × 3 × 2 = 36

Answer: (b)

? = $√{({272}^2 - {128}^2)}$

= $√{(272 + 128)(272 + 128)}$

= $√{400 × 144}$ = 20 × 12 = 240

Answer: (d)

${(0.03)^2 - (0.01)^2}/{0.03 - 0.01}$

[Using ${a^2 - b^2}$ = (a + b)(a - b)]

= ${(0.03 + 0.01)(0.03 - 0.01)}/{0.03 - 0.01}$

= 0.03 + 0.01 = 0.04

Using Rule 8,

${(0.03)^2 - (0.01)^2}/{0.03 - 0.01}$

= (0.03 + 0.01 = 0.04