simplify the expression

Question

√15(√6+6)

Answer 1

Given expression is √15(√6+6)

                               = √15(√6) + √15(6)

                               = √(15 * 6) + 6√15

                               = √(3*5*3*2) + 6√(3*5)            [Split into factors]

                               = 3√(5*2) + 6√(3*5)

                               = 3√5 ( √2 + 2√3)

                               = 3√5 [1.414 + 2(1.7320)]      [Since √2 = 1.414 and √3 = 1.7320]

                               = 3√5 [1.414 + 3.436 ]

                               = 3(2.2360)(4.878)                    [Since √5 = 2.2360]

                               = 32.7216

Therefore √15(√6+6) = 32.7216.