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sqrt10(sqrt30+sqrt15)

10(30+15) \sqrt{10}(\sqrt{30}+\sqrt{15})

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Full solution

Q. 10(30+15) \sqrt{10}(\sqrt{30}+\sqrt{15})
  1. Distribute square roots: First, distribute 10\sqrt{10} to both 30\sqrt{30} and 15\sqrt{15}. So, 10(30+15)=10×30+10×15\sqrt{10}(\sqrt{30}+\sqrt{15}) = \sqrt{10}\times\sqrt{30} + \sqrt{10}\times\sqrt{15}.
  2. Multiply square roots: Now, multiply the square roots. 10×30=10×30=300\sqrt{10}\times\sqrt{30} = \sqrt{10\times30} = \sqrt{300}. 10×15=10×15=150\sqrt{10}\times\sqrt{15} = \sqrt{10\times15} = \sqrt{150}.
  3. Simplify square roots: Simplify the square roots. 300\sqrt{300} can be written as 100×3=100×3=103\sqrt{100\times3} = \sqrt{100}\times\sqrt{3} = 10\sqrt{3}. 150\sqrt{150} can be written as 25×6=25×6=56\sqrt{25\times6} = \sqrt{25}\times\sqrt{6} = 5\sqrt{6}.
  4. Add simplified square roots: Add the simplified square roots. 103+5610\sqrt{3} + 5\sqrt{6}.
  5. Final answer: There's no further simplification possible, so this is the final answer.

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