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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 the expression, first calculate ( 4.8^8 ) and ( 3.6^6 ):
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Calculate ( 4.8^8 ): [ 4.8^8 = 65536 ]
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Calculate ( 3.6^6 ): [ 3.6^6 = 729 ]
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Add the results: [ 65536 + 729 = 66265 ]
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Now, divide by 4: [ \frac{66265}{4} = 16566.25 ]
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Finally, take the square root: [ \sqrt{16566.25} = 128.7 \approx 3 ]
Step 2
b) \( \frac{1}{(2 \times 10^4) + (5 \times 10^3)} \)
Answer
First, simplify the expression inside the denominator:
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Calculate the two parts:
- First part: ( 2 \times 10^4 = 20000 )
- Second part: ( 5 \times 10^3 = 5000 )
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Add the two values: [ 20000 + 5000 = 25000 ]
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Now compute the final answer: [ \frac{1}{25000} = 0.00004 ]