model 4 simplifying roots with values Section-Wise Topic Notes With Detailed Explanation And Example Questions

Answer: (c)

Expression

$16√{3/4} - 9√{4/3}$ if $√12$ = 3.46

=$16√{{3×4}/{4×4}} - 9√{{4×3}/{3×3}}$

=${16√12}/4-{9√12}/3$

=$4√12-3√12$

=$√12$=3.46

Answer: (c)

$√8 +2√32 -3√128 +4√50$

=$2√2 +8√2 -3×8√2 +4×5√2$

=$2√2 +8√2 -24√2 +20√2$

= (2 + 8 -24 +20)$√2$

=6$√2$=6×1.414=8.484

Answer: (d)

Expression=${3√5}/{2√5 -0.48}$

=${3×2.24}/{2×2.24-0.48}={6.72}/{4.48-0.48}$

=$6.72/4=1.68$

Answer: (d)

$√5/2 + 5/{3√5} - √45$

=$√5/2+{5×√5}/{3×5}-3√5$

=$√5/2+√5/3-3√5$

=${3√5+2√5-18√5}/6$

=${-13√5}/6={-13×2.236}/6$

=${-29.068}/6=-4.845$

Answer: (d)

$√33$ = 5.745(Given)

$√{3/11}=√{{3×11}/{11×11}}=√33/11$

=${5.745}/11 ≈0.5223$

Answer: (a)

Expression

=${3 +√6}/{5√3 - 2√12- √32+√ 50}$

=${3 +√6}/{5√3 - 2√{2×2×3}- √{2×2×2×2×2}+√{2×5×5}}$

=${3 +√6}/{5√3 - 4√{3}- 4√{2}+5√{2}}$

=${3 +√6}/{√3 +√2}={(3+√6)(√3-√2)}/{(√3+√2)(√3-√2)}$

[On rationalising the denominator]

=${3√3+√18-3√2-√12}/{3-2}$

=$3√3+3√2-3√2-2√3$

=$√3=1.732$