Carol says that 64^{ rac{1}{2}} = rac{1}{32} - OCR - GCSE Maths - Question 12 - 2018 - Paper 1
Question 12
Carol says that 64^{ rac{1}{2}} = rac{1}{32}.
Explain her error and give the correct value of 64^{ rac{1}{2}} in the form \frac{p}{q}.
Worked Solution & Example Answer:Carol says that 64^{ rac{1}{2}} = rac{1}{32} - OCR - GCSE Maths - Question 12 - 2018 - Paper 1
Step 1
Explain her error
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Answer
Carol's mistake lies in the misunderstanding of the operation involved in taking the square root of a number. Instead of correctly applying the square root function to 64, she incorrectly divided the exponent by 2, which does not yield the proper square root value. The correct operation for finding the square root is to apply it directly to the number rather than manipulating the exponent.
Step 2
Give the correct value of 64^{ rac{1}{2}}
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Answer
To find the correct value of 64^{ rac{1}{2}}, we calculate the square root of 64. [64^{ rac{1}{2}} = \sqrt{64} = 8.] Thus, in the form \frac{p}{q}, we can express this as \frac{8}{1}.
