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slava [35]
2 years ago
15

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

Mathematics
2 answers:
alexandr402 [8]2 years ago
7 0

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


Dvinal [7]2 years ago
7 0

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}

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