Question

Simplify the following 3√28-5√63+4√112

Answer 1

7√7

using the ' rule of radicals '

• √a × √b ⇔ √ab

simplifying the radicals

√28 = √(4 × 7 ) = √4 × √7 = 2√7

√63 = √(9 × 7) =√9 × √7 = 3√7

√112 = √(16 × 7 ) = √16 × √7 = 4√7

substituting into the expression

3(2√7) - 5(3√7) + 4(4√7) = 6√7 - 15√7 + 16√7 = 7√7

Answer 2

First, simply each term.  Then, add the coefficients of the like terms (same radicals).

$3\sqrt{28} = 3\sqrt{2*2*7} = 3(2)\sqrt{7} = 6\sqrt{7}$

$5\sqrt{63} = 5\sqrt{3*3*7} = 5(3)\sqrt{7} = 15\sqrt{7}$

$4\sqrt{112} = 4\sqrt{2*2*2*2*7} = 4(2*2)\sqrt{7} = 16\sqrt{7}$

*********************************************************

$3\sqrt{28} - 5\sqrt{63} + 4\sqrt{112}$

= $6\sqrt{7} - 15\sqrt{7} + 16\sqrt{7}$

= $(6 - 15 + 16)\sqrt{7}$

= $7\sqrt{7}$