Question

Operations with Radical Expressions

Answer 1

Answer: $30\sqrt{11}$

Step-by-step explanation:

  $3\sqrt{50} * \sqrt{22}$

= $3\sqrt{5*5*2} * \sqrt{2*11}$

= $3\sqrt{5*5*2*2*11}$

= $3*5*2\sqrt{11}$

= $30\sqrt{11}$

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Answer: $6\sqrt{30}$

Step-by-step explanation:

  $\sqrt{20} * \sqrt{3} * \sqrt{18}$

= $\sqrt{2*2*5} * \sqrt{3} * \sqrt{3*3*2}$

= $\sqrt{2*2*5*3*3*3*2}$

= $2*3\sqrt{5*3*2}$

= $6\sqrt{30}$

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Answer: $-\sqrt{5}$

Step-by-step explanation:

  $4\sqrt{20} - 3\sqrt{45}$

= $4\sqrt{2*2*5} - 3\sqrt{3*3*5}$

= $4*2\sqrt{5} - 3*3\sqrt{5}$

= $8\sqrt{5} - 9\sqrt{5}$

= $-\sqrt{5}$

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Answer: $4\sqrt{5}$

Step-by-step explanation:

  $2\sqrt{5} + 3\sqrt{5} - \sqrt{5}$

= $(2+3-1)\sqrt{5}$

= $4\sqrt{5}$

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Answer: $46\sqrt{2}$

Step-by-step explanation:

  $4\sqrt{32} + 6\sqrt{50}$

= $4\sqrt{2*2*2*2*2} + 6\sqrt{2*5*5}$

= $4*2*2\sqrt{2} + 6*5\sqrt{2}$

= $16\sqrt{2} + 30\sqrt{2}$

= $46\sqrt{2}$