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(sqrt8+sqrt12)(sqrt48+sqrt18)=

1919. (8+12)(48+18)= (\sqrt{8}+\sqrt{12})(\sqrt{48}+\sqrt{18})=

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Full solution

Q. 1919. (8+12)(48+18)= (\sqrt{8}+\sqrt{12})(\sqrt{48}+\sqrt{18})=
  1. Simplify square roots: First, let's simplify each square root. 8=4×2=22\sqrt{8} = \sqrt{4\times2} = 2\sqrt{2}
  2. Substitute simplified roots: 12=4×3=23\sqrt{12} = \sqrt{4\times3} = 2\sqrt{3}
  3. Use distributive property: 48=16×3=43\sqrt{48} = \sqrt{16\times3} = 4\sqrt{3}
  4. Multiply terms: 18=9×2=32\sqrt{18} = \sqrt{9\times2} = 3\sqrt{2}
  5. Multiply terms: 18=9×2=32\sqrt{18} = \sqrt{9\times 2} = 3\sqrt{2} Now, substitute the simplified square roots back into the original expression.\newline(22+23)(43+32)(2\sqrt{2} + 2\sqrt{3})(4\sqrt{3} + 3\sqrt{2})
  6. Multiply terms: 18=9×2=32\sqrt{18} = \sqrt{9\times2} = 3\sqrt{2} Now, substitute the simplified square roots back into the original expression.\newline(22+23)(43+32)(2\sqrt{2} + 2\sqrt{3})(4\sqrt{3} + 3\sqrt{2}) Use the distributive property (FOIL) to multiply the terms.\newline22×43+22×32+23×43+23×322\sqrt{2}\times4\sqrt{3} + 2\sqrt{2}\times3\sqrt{2} + 2\sqrt{3}\times4\sqrt{3} + 2\sqrt{3}\times3\sqrt{2}
  7. Multiply terms: 18=9×2=32\sqrt{18} = \sqrt{9\times2} = 3\sqrt{2} Now, substitute the simplified square roots back into the original expression.\newline(22+23)(43+32)(2\sqrt{2} + 2\sqrt{3})(4\sqrt{3} + 3\sqrt{2}) Use the distributive property (FOIL) to multiply the terms.\newline22×43+22×32+23×43+23×322\sqrt{2}\times4\sqrt{3} + 2\sqrt{2}\times3\sqrt{2} + 2\sqrt{3}\times4\sqrt{3} + 2\sqrt{3}\times3\sqrt{2} Multiply the terms.\newline86+6×2+8×3+668\sqrt{6} + 6\times2 + 8\times3 + 6\sqrt{6}

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