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AQA GCSE · Question 01 · Number
Work out 12² ÷ (1/3 × √36)
Work out 12² ÷ (1/3 × √36)
How to approach this question
First, evaluate the expression inside the brackets. Find the square root of 36. Then, multiply that result by 1/3. Next, calculate 12 squared. Finally, divide the result of 12 squared by the result from the brackets.
Full Answer
Step 1: Calculate the values inside the bracket.
√36 = 6
1/3 × 6 = 6/3 = 2
Step 2: Calculate 12².
12² = 144
Step 3: Perform the division.
144 ÷ 2 = 72
Answer: 72
This question tests your understanding of the order of operations, often remembered by the acronym BIDMAS or PEMDAS.
B - Brackets: We must evaluate the expression inside the brackets first: (1/3 × √36).
I - Indices: Inside the brackets, we have a square root, which is a type of index. √36 = 6.
M - Multiplication: Now we do the multiplication inside the bracket: 1/3 × 6 = 2.
So the expression becomes 12² ÷ 2.
Next, we evaluate the other index: 12² = 144.
Finally, we do the division: 144 ÷ 2 = 72.
Common mistakes
✗ A common mistake is to not follow BIDMAS correctly. For example, doing 144 ÷ 1/3 before multiplying by √36.
✗ Another error is calculating 1/3 of 36 instead of 1/3 of √36.
✗ Forgetting that √36 has a value of 6.
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