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Calculate. (a) \( \sqrt{\frac{4.8^8 + 3.6^6}{4}} \) (b) \( \frac{1}{(2 \times 10^4) + (5 \times 10^3)} \) - OCR - GCSE Maths - Question 1 - 2017 - Paper 1
Question 1
Calculate. (a) \( \sqrt{\frac{4.8^8 + 3.6^6}{4}} \) (b) \( \frac{1}{(2 \times 10^4) + (5 \times 10^3)} \)
Worked Solution & Example Answer:Calculate. (a) \( \sqrt{\frac{4.8^8 + 3.6^6}{4}} \) (b) \( \frac{1}{(2 \times 10^4) + (5 \times 10^3)} \) - OCR - GCSE Maths - Question 1 - 2017 - Paper 1
Step 1
(a) \( \sqrt{\frac{4.8^8 + 3.6^6}{4}} \)
Answer
To solve this expression, we first calculate the numerator:
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Calculate ( 4.8^8 ):
- ( 4.8^8 = 659181696 ).
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Calculate ( 3.6^6 ):
- ( 3.6^6 = 729 ).
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Add the results:
- ( 659181696 + 729 = 659182425 ).
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Now divide by 4:
- ( \frac{659182425}{4} = 164795606.25 ).
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Finally, take the square root:
- ( \sqrt{164795606.25} = 4061.37 ) (approx).
Thus, the answer is approximately 4061.37.
Step 2
(b) \( \frac{1}{(2 \times 10^4) + (5 \times 10^3)} \)
Answer
First, evaluate the expression in the denominator:
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Calculate ( 2 \times 10^4 = 20000 ).
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Calculate ( 5 \times 10^3 = 5000 ).
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Add these values:
- ( 20000 + 5000 = 25000 ).
Next, calculate the final answer:
- Now find the reciprocal:
- ( \frac{1}{25000} = 0.00004 ).
Therefore, the final answer is ( 0.00004 ).