Reece is given this question - OCR - GCSE Maths - Question 13 - 2021 - Paper 1
Question 13
Reece is given this question.
Write 20 as a product of prime factors.
Give your answer in index form.
Reece's answer is $2 \times 2 \times 5$.
Is Reece correct?
E... show full transcript
Worked Solution & Example Answer:Reece is given this question - OCR - GCSE Maths - Question 13 - 2021 - Paper 1
Step 1
Write 20 as a product of prime factors. Give your answer in index form.
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Answer
To express 20 as a product of prime factors, we can start by dividing by the smallest prime number:
Divide 20 by 2: ( 20 \div 2 = 10 )
Divide 10 by 2: ( 10 \div 2 = 5 )
Since 5 is a prime number, we cannot divide further.
Thus, the prime factorization of 20 is: ( 20 = 2^2 \times 5^1 ).
In index form, the answer is: ( 20 = 2^2 \times 5 ).
Reece's answer 2×2×5 is correct, but it should be expressed as ( 2^2 \times 5 ).
Step 2
Complete the power of 2.
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Answer
Given the equation (\frac{1}{8} = 2^{_}), we can rewrite 8 as a power of 2: ( 8 = 2^3 ). Therefore, (\frac{1}{8} = 2^{-3}). So, we get:
(\frac{1}{8} = 2^{-3} ). Thus, the blank should be filled with -3.
Step 3
Work out. \(\sqrt{81} \times 2^3\)
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Answer
First, we calculate (\sqrt{81}):
(\sqrt{81} = 9 ).
Now, calculate (2^3):
(2^3 = 8 ).
Now, multiply the two results together:
(9 \times 8 = 72).
