Questions: What is the square root of 5.94 times 10 to the power of 15? Give your answer to 3 significant figures.

What is the square root of 5.94 times 10 to the power of 15? Give your answer to 3 significant figures.
Transcript text: quesicion 4 What is $\sqrt{5.94 \times 10^{15}}$ ? Give your answer to 3 significant figures.
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Solution

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Solution Steps

Step 1: Rewrite the expression in scientific notation

The given expression is \( \sqrt{5.94 \times 10^{15}} \). To simplify, rewrite the expression as: \[ \sqrt{5.94 \times 10^{15}} = \sqrt{5.94} \times \sqrt{10^{15}}. \]

Step 2: Simplify the square root of the coefficient

Calculate \( \sqrt{5.94} \): \[ \sqrt{5.94} \approx 2.437. \]

Step 3: Simplify the square root of the power of 10

Calculate \( \sqrt{10^{15}} \): \[ \sqrt{10^{15}} = 10^{15/2} = 10^{7.5}. \]

Step 4: Combine the results

Multiply the results from Step 2 and Step 3: \[ 2.437 \times 10^{7.5}. \]

Step 5: Express in standard form

Convert \( 10^{7.5} \) to standard form: \[ 10^{7.5} = 10^{7} \times 10^{0.5} = 10^{7} \times \sqrt{10} \approx 10^{7} \times 3.162. \] Thus: \[ 2.437 \times 10^{7.5} \approx 2.437 \times 3.162 \times 10^{7} \approx 7.706 \times 10^{7}. \]

Step 6: Round to 3 significant figures

Round \( 7.706 \times 10^{7} \) to 3 significant figures: \[ 7.71 \times 10^{7}. \]

Final Answer

\(\boxed{7.71 \times 10^{7}}\)

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