Question

Given that root 3 = 1.732, find root 75 + 1/2 root 48 - root 192

Answer 1

Answer:

-1.732

Step-by-step explanation:

By prime factorization,

75=5×5×3

48=2×2×2×2×3

192=2×2×2×2×2×2×3

Hence,

√75=5×√3=5√3

√48=2×2×√3=4√3

√192=2×2×2×√3=6√3

Thus,

(√75) + (1/2√48) - (√192)

=5√3 + (1/2)×4√3 - 8√3

=5√3 + 2√3 - 8√3

=√3(5+2-8)

=√3×(-1)

=-√3

=-1.732