Match the radical with the simplified version.(6 points)

Question

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98x5y−−−−−√
49x3y4−−−−−−√
36y4−−−−√
9x2−−−√
18x5y3−−−−−−√
100x2y3−−−−−−−√
10xyy√6y23x2y2xy−−−√7x22xy−−−√3x7xy2x−−√

Answer 1

To match the radicals with their simplified versions, we first need to simplify each radical one by one. Here are the simplifications:

1. √98x⁵y:

   • 98 = 49 * 2, so √98 = √(49 * 2) = 7√2.
   • For x⁵ = x⁴ * x, so √(x⁵) = x²√x.
   • The radical simplifies to 7x²√(2xy).

2. √49x³y⁴:

   • 49 = 7², so √49 = 7.
   • For x³ = x² * x, so √(x³) = x√x.
   • For y⁴ = (y²)², so √(y⁴) = y².
   • The radical simplifies to 7x√x * y² = 7x²y²√x.

3. √36y⁴:

   • 36 = 6², so √36 = 6.
   • For y⁴ = (y²)², so √(y⁴) = y².
   • The radical simplifies to 6y².

4. √9x²:

   • 9 = 3², so √9 = 3.
   • For x² = (x)², so √(x²) = x.
   • The radical simplifies to 3x.

5. √(18x⁵y³):

   • 18 = 9 * 2, so √18 = 3√2.
   • For x⁵ = x⁴ * x, so √(x⁵) = x²√x.
   • For y³ = y² * y, so √(y³) = y√y.
   • The radical simplifies to 3x²y√(2xy).

6. √(100x²y³):

   • 100 = 10², so √100 = 10.
   • For x² = (x)², so √(x²) = x.
   • For y³ = y² * y, so √(y³) = y√y.
   • The radical simplifies to 10xy√y.

So the simplified forms for the radicals are:

• √98x⁵y matches with 10xy√6y².
• √49x³y⁴ matches with 7x²y²√x.
• √36y⁴ matches with 6y².
• √9x² matches with 3x.
• √(18x⁵y³) matches with 10xy√6y².
• √(100x²y³) matches with 10xy√y.

Thus, the final matches are:

1. √98x⁵y → 10xy√6y²
2. √49x³y⁴ → 7x²y²√x
3. √36y⁴ → 6y²
4. √9x² → 3x
5. √(18x⁵y³) → 10xy√6y²
6. √(100x²y³) → 10xy√y