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

Answer: (c)

$√{5+ √{11 + √{19 + √{29 + √{49}}}}}$

$√{5+ √{11 + √{19 + √{29 + 7}}}}$

$√{5+ √{11 + √{19 + 6}}}$

$√{5+ √{11 + √{25}}}$

$√{5+ √{11 + 5}}$

$√{5+ 4} = √9$ = 3

Answer: (d)

${1/{3 - √8}} = {3 + √8}/{(3 - √8)(3 + √8)}$

(Rationalising the denominator)

= ${3 + √8}/{9 - 8} = 3 + √8$

Expression

= $3 + √{8} + 3 + √{8} - 6 - 4√{2}$

= $6 + 2√{8} - 6 - 4√{2} = 2√{8} - 4√{2}$

= $2 × 2√{2} - 4√{2} = 0$

Answer: (b)

$√{1.3} + √{1300} + √0.013$

= $√{{130}/{100}} +10√{13} + √{{130}/{10000}}$

= $1/10√{130} + 10√{13} + 1/100√{130}$

= ${11.40}/10 + 3.605 × 10 + {11.40}/100$

= 1.140 + 36.05 + 0.1140

= 37.304

Answer: (d)

Expression

=$√{{0.081 × 0.484}/{0.0064 × 6.25}}$

= $√{{81 × 484}/{64 × 625}} = {9 × 22}/{8 × 25} = 0.99$

Answer: (b)

$√{{0.342 × 0.684}/{0.000342 × 0.000171}}$

= $√{{342 × 684 × {10}^6}/{342 × 171}}$

= $√{4 × {10}^6} = 2 × {10}^3$ = 2000