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45−320+45\sqrt{45} -3 \sqrt{20} +4\sqrt{5}

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Full solution

Q. 45−320+45\sqrt{45} -3 \sqrt{20} +4\sqrt{5}
  1. Simplify 45\sqrt{45}: First, let's simplify each square root separately.45\sqrt{45} can be written as (9×5)\sqrt{(9\times5)} which simplifies to 353\sqrt{5} because 9\sqrt{9} is 33.
  2. Simplify 20\sqrt{20}: Next, simplify 20\sqrt{20}.20\sqrt{20} can be written as (4×5)\sqrt{(4\times5)} which simplifies to 252\sqrt{5} because 4\sqrt{4} is 22.
  3. Multiply 20\sqrt{20} by 33: Now, multiply the simplified square root of 2020 by 33.3×253 \times 2\sqrt{5} equals 656\sqrt{5}.
  4. Combine terms with 5\sqrt{5}: Finally, combine all the terms with 5\sqrt{5}.\newlineSo, we have 35−65+453\sqrt{5} - 6\sqrt{5} + 4\sqrt{5}.
  5. Add and subtract coefficients: Add and subtract the coefficients of 5\sqrt{5}. 3−6+43 - 6 + 4 equals 11. So, the final answer is 151\sqrt{5}, which is just 5\sqrt{5}.

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