Question

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Explanation:

Step1: Find square root of 100

$\sqrt{100}=10$

Step2: Find square root of $9x^2$

$\sqrt{9x^2}=\sqrt{9}\cdot\sqrt{x^2}=3x$

Step3: Find square root of $\frac{1}{4}x^2$

$\sqrt{\frac{1}{4}x^2}=\sqrt{\frac{1}{4}}\cdot\sqrt{x^2}=\frac{1}{2}x$

Step4: Simplify $x\cdot x$ first, then find root

$x\cdot x=x^2$, $\sqrt{x^2}=x$

Step5: Simplify $7x\cdot7x$ first, then find root

$7x\cdot7x=(7x)^2$, $\sqrt{(7x)^2}=7x$

Step6: Recognize repeated factor

$(2x-9)(2x-9)=(2x-9)^2$, so the base is $2x-9$

Answer:

1. $10$
2. $3x$
3. $\frac{1}{2}x$
4. $x$
5. $7x$
6. $2x-9$