Math Problem Statement

8√8 + 3√2 + 3√12

Solution

Let's simplify each term first:

  1. 888\sqrt{8}:
    Break down 8\sqrt{8} as follows:
    8=4×2=22\sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2}
    Now, substitute back into 888\sqrt{8}:
    88=8×22=1628\sqrt{8} = 8 \times 2\sqrt{2} = 16\sqrt{2}

  2. 323\sqrt{2}:
    This term is already simplified.

  3. 3123\sqrt{12}:
    Break down 12\sqrt{12} as follows:
    12=4×3=23\sqrt{12} = \sqrt{4 \times 3} = 2\sqrt{3}
    Now, substitute back into 3123\sqrt{12}:
    312=3×23=633\sqrt{12} = 3 \times 2\sqrt{3} = 6\sqrt{3}

Now, putting it all together: 88+32+312=162+32+638\sqrt{8} + 3\sqrt{2} + 3\sqrt{12} = 16\sqrt{2} + 3\sqrt{2} + 6\sqrt{3}

Combine like terms: (162+32)+63=192+63(16\sqrt{2} + 3\sqrt{2}) + 6\sqrt{3} = 19\sqrt{2} + 6\sqrt{3}

Thus, the simplified expression is: 192+6319\sqrt{2} + 6\sqrt{3}

Would you like more details on the simplification process or another explanation?

Here are 5 related questions:

  1. How would you simplify 518+285\sqrt{18} + 2\sqrt{8}?
  2. What is 50+2\sqrt{50} + \sqrt{2}?
  3. How do you factor and simplify 72\sqrt{72}?
  4. What is the result of combining 73+2127\sqrt{3} + 2\sqrt{12}?
  5. How do you simplify 432+524\sqrt{32} + 5\sqrt{2}?

Tip: Always look for perfect squares within the square root to simplify expressions efficiently!

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Math Problem Analysis

Mathematical Concepts

Radicals
Simplifying Square Roots
Combining Like Terms

Formulas

√(a × b) = √a × √b
a√n + b√n = (a + b)√n

Theorems

Properties of Square Roots
Simplification of Radicals

Suitable Grade Level

Grades 9-10