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Simplify.
sqrt((2-sqrt3)sqrt(7+4sqrt3))

Simplify.\newline(23)7+43 \sqrt{(2-\sqrt{3}) \sqrt{7+4 \sqrt{3}}}

Full solution

Q. Simplify.\newline(23)7+43 \sqrt{(2-\sqrt{3}) \sqrt{7+4 \sqrt{3}}}
  1. Use Property of Square Roots: We are given the expression (23)7+43\sqrt{(2-\sqrt{3}) \cdot \sqrt{7+4\sqrt{3}}}. To simplify this, we can use the property of square roots that states ab=ab\sqrt{a} \cdot \sqrt{b} = \sqrt{a \cdot b}.
  2. Multiply Quantities: Now, let's multiply the two quantities inside the square roots together.\newline(23)×(7+43)=2×7+2×433×73×43(2 - \sqrt{3}) \times (7 + 4\sqrt{3}) = 2\times7 + 2\times4\sqrt{3} - \sqrt{3}\times7 - \sqrt{3}\times4\sqrt{3}
  3. Perform Multiplications: Perform the multiplications. 14+83734×314 + 8\sqrt{3} - 7\sqrt{3} - 4\times 3
  4. Combine Like Terms: Combine like terms and simplify. 14+837312=1412+837314 + 8\sqrt{3} - 7\sqrt{3} - 12 = 14 - 12 + 8\sqrt{3} - 7\sqrt{3}
  5. Further Simplification: Further simplification gives us: 2+32 + \sqrt{3}
  6. Take Square Root: Now we take the square root of the simplified expression. 2+3\sqrt{2 + \sqrt{3}}