Question

algebra i-study guide

1. $sqrt{16.93 - 12.78} =$
2. $sqrt{\frac{1}{2}} cdot sqrt{\frac{1}{4}} =$
3. $sqrt{5} - sqrt{16} \times sqrt{8} =$
4. $sqrt{200} sqrt{2} =$
5. $sqrt{0.09}sqrt{0.25} =$
6. $sqrt{7} - sqrt{15} =$

Explanation:

Step1: Calculate inside the square root

$16.93 - 12.78 = 4.15$

Step2: Take square root of result

$\sqrt{4.15} \approx 2.04$

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Step1: Multiply radicands first

$\sqrt{\frac{1}{2} \times \frac{1}{4}} = \sqrt{\frac{1}{8}}$

Step2: Simplify the radical

$\sqrt{\frac{1}{8}} = \frac{1}{2\sqrt{2}} = \frac{\sqrt{2}}{4} \approx 0.35$

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Step1: Simplify individual radicals

$\sqrt{16}=4$, $\sqrt{8}=2\sqrt{2}$

Step2: Perform multiplication first

$4 \times 2\sqrt{2} = 8\sqrt{2}$

Step3: Subtract from $\sqrt{5}$

$\sqrt{5} - 8\sqrt{2} \approx 2.24 - 11.31 = -9.07$

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Step1: Multiply radicands first

$\sqrt{200 \times 2} = \sqrt{400}$

Step2: Evaluate the square root

$\sqrt{400} = 20$

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Step1: Simplify individual radicals

$\sqrt{0.09}=0.3$, $\sqrt{0.25}=0.5$

Step2: Multiply the results

$0.3 \times 0.5 = 0.15$

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Step1: Approximate each square root

$\sqrt{7} \approx 2.65$, $\sqrt{15} \approx 3.87$

Step2: Subtract the values

$2.65 - 3.87 = -1.22$

Answer:

1. $\approx 2.04$
2. $\frac{\sqrt{2}}{4} \approx 0.35$
3. $\sqrt{5} - 8\sqrt{2} \approx -9.07$
4. $20$
5. $0.15$
6. $\approx -1.22$