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Simplify: 5sqrt162-3sqrt18÷4sqrt98

Simplify: \newline5162−318÷4985\sqrt{162}-3\sqrt{18}\div 4\sqrt{98}

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Full solution

Q. Simplify: \newline5162−318÷4985\sqrt{162}-3\sqrt{18}\div 4\sqrt{98}
  1. Simplify Square Roots: Simplify each square root term separately.\newline5162=5(81×2)=5×92=4525\sqrt{162} = 5\sqrt{(81\times2)} = 5\times9\sqrt{2} = 45\sqrt{2},\newline318=3(9×2)=3×32=923\sqrt{18} = 3\sqrt{(9\times2)} = 3\times3\sqrt{2} = 9\sqrt{2},\newline498=4(49×2)=4×72=2824\sqrt{98} = 4\sqrt{(49\times2)} = 4\times7\sqrt{2} = 28\sqrt{2}.
  2. Perform Division: Perform the division next.\newline(92)÷(282)=928(9\sqrt{2}) \div (28\sqrt{2}) = \frac{9}{28}.
  3. Combine Results: Combine the results.\newline452−(928)45\sqrt{2} - \left(\frac{9}{28}\right),\newlineSince 45245\sqrt{2} is not like terms with 928\frac{9}{28}, they can't be directly subtracted.

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