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in the space prov b {:[3sqrt8-sqrt18],[3sqrt8-3sqrt3]:}

in the space prov\newlineb\newline38−1838−33 \begin{array}{l} 3 \sqrt{8}-\sqrt{18} \\ 3 \sqrt{8}-3 \sqrt{3} \end{array}

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Checkpoint: Rational and irrational numbersright chevron icon

Full solution

Q. in the space prov\newlineb\newline38−1838−33 \begin{array}{l} 3 \sqrt{8}-\sqrt{18} \\ 3 \sqrt{8}-3 \sqrt{3} \end{array}
  1. Simplify 8\sqrt{8}: First, let's simplify 8\sqrt{8} and 18\sqrt{18} individually.\newline8=(4⋅2)=4⋅2=22\sqrt{8} = \sqrt{(4\cdot2)} = \sqrt{4} \cdot \sqrt{2} = 2\sqrt{2}.
  2. Simplify 18\sqrt{18}: Now, simplify 18\sqrt{18}.18=(9⋅2)=9⋅2=32\sqrt{18} = \sqrt{(9\cdot2)} = \sqrt{9} \cdot \sqrt{2} = 3\sqrt{2}.
  3. Substitute and Simplify: Substitute the simplified forms back into the original expression. 38−183\sqrt{8} - \sqrt{18} becomes 3∗(22)−32.3*(2\sqrt{2}) - 3\sqrt{2}.
  4. Multiply and Simplify: Multiply 33 by 222\sqrt{2} to simplify further.\newline3×(22)=623\times(2\sqrt{2}) = 6\sqrt{2}.
  5. Combine Like Terms: Now we have 62−326\sqrt{2} - 3\sqrt{2}. Since they are like terms, we can subtract the coefficients. 62−32=(6−3)26\sqrt{2} - 3\sqrt{2} = (6-3)\sqrt{2}.
  6. Perform Subtraction: Perform the subtraction.\newline(6−3)2=32(6-3)\sqrt{2} = 3\sqrt{2}.

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