Samuel has tried to work out 6√30 ÷ 2 but has made a mistake. His workings are shown below. a) Work out 6√30 ÷ 2. Give your answer as an integer or as a surd in its simplest form.... Samuel has tried to work out 6√30 ÷ 2 but has made a mistake. His workings are shown below. a) Work out 6√30 ÷ 2. Give your answer as an integer or as a surd in its simplest form. b) Write a sentence to explain the mistake that Samuel has made.
Understand the Problem
The question is asking us to perform a calculation involving the expression 6√30 ÷ 2 and identify the mistake made by Samuel in his workings. We need to compute the value of the expression and provide an explanation for the error.
Answer
$3\sqrt{30}$
Answer for screen readers
The final answer is $3\sqrt{30}$.
Steps to Solve
- Identify the Expression
We need to evaluate the expression $6\sqrt{30} \div 2$.
- Divide the Coefficient
First, divide the coefficient 6 by 2:
$$ \frac{6}{2} = 3 $$
This step simplifies the expression.
- Simplify the Expression
Now, rewrite the expression using the result from the previous step:
$$ 3\sqrt{30} $$
This gives us the final form.
- State the Final Answer
The answer is expressed as $3\sqrt{30}$.
- Identify the Mistake
Samuel made a mistake by incorrectly writing the division as $6 \div 2 \times \sqrt{30 \div 2}$. The square root should not be calculated separately in division with constants; the division should be done first.
The final answer is $3\sqrt{30}$.
More Information
The result $3\sqrt{30}$ represents the simplest form of the original expression. It maintains the surd, which is often needed in mathematical expressions.
Tips
Samuel mistakenly treated the division as if it could apply separately to the square root. It's crucial to remember that operations on coefficients and radicals should be handled carefully to avoid errors.
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