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-3sqrt112+10sqrt112

−3112+10112 -3 \sqrt{112}+10 \sqrt{112}

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Full solution

Q. −3112+10112 -3 \sqrt{112}+10 \sqrt{112}
  1. Factor out common square root: Factor out the common square root from both terms.\newline−3112+10112-3\sqrt{112} + 10\sqrt{112} can be written as (−3+10)112(-3 + 10)\sqrt{112}.
  2. Simplify coefficients: Simplify the coefficients.\newline(−3+10)=7(-3 + 10) = 7.
  3. Multiply coefficient by square root: Multiply the simplified coefficient by the square root. 7×1127 \times \sqrt{112} is the simplified form of the expression.
  4. Simplify square root factors: Simplify 112\sqrt{112} by finding perfect square factors.\newline112112 can be factored into 16×716 \times 7, where 1616 is a perfect square.
  5. Take square root of perfect square: Take the square root of the perfect square factor. 16=4\sqrt{16} = 4, so 112=4×7\sqrt{112} = 4 \times \sqrt{7}.
  6. Multiply coefficient by square root: Multiply the coefficient by the simplified square root.\newline7×4×77 \times 4 \times \sqrt{7} equals 28×728 \times \sqrt{7}.

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