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Combine the like terms under the square root.

Biology

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Answers

3 parts
1.1

6x\text{6x}

1.2

\text{5a^2b^3}

1.3

\text{8x - 3x^2}

Step-by-step solution

6 steps

Here are the solutions to the problems:

Part 1.1· 2 steps

  1. Combine the like terms under the square root.

    100x2−64x2=36x2\sqrt{100x^2 - 64x^2} = \sqrt{36x^2}
  2. Take the square root of the expression.

    36x2=36⋅x2=6∣x∣\sqrt{36x^2} = \sqrt{36} \cdot \sqrt{x^2} = 6|x|

    The absolute value is used because x2\sqrt{x^2} is ∣x∣|x|. If xx is assumed to be non-negative, then it simplifies to 6x6x. Assuming x≥0x \ge 0:

    36x2=6x\sqrt{36x^2} = 6x

    The final answer is 6x\boxed{\text{6x}}

Part 1.2

\text{5a^2b^3}

  1. Combine the like terms under the square root.

    9a4b6+16a4b6=25a4b6\sqrt{9a^4b^6 + 16a^4b^6} = \sqrt{25a^4b^6}
  2. Take the square root of the expression.

    25a4b6=25⋅a4⋅b6=5⋅a4/2⋅b6/2=5a2b3\sqrt{25a^4b^6} = \sqrt{25} \cdot \sqrt{a^4} \cdot \sqrt{b^6} = 5 \cdot a^{4/2} \cdot b^{6/2} = 5a^2b^3

    The final answer is \boxed{\text{5a^2b^3}}

Part 1.3

\text{8x - 3x^2}

  1. Take the square root of the first term.

    64x2=64⋅x2=8∣x∣\sqrt{64x^2} = \sqrt{64} \cdot \sqrt{x^2} = 8|x|

    Assuming x≥0x \ge 0:

    64x2=8x\sqrt{64x^2} = 8x
  2. Subtract the second term from the result.

    8x−3x28x - 3x^2

    The final answer is \boxed{\text{8x - 3x^2}}

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