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Rationalising the denominator of 6 divided by the square root of 3 gives which expression?
A3 times the square root of 2
B6 times the square root of 3
CThe square root of 18
D2 times the square root of 3
Answer & Solution
Correct answer: D. 2 times the square root of 3
1. The denominator holds a surd, so the fraction is rewritten with a rational denominator.
2. Multiply the fraction by the square root of 3 over the square root of 3.
3. That value is equal to 1, so the value of the fraction does not change.
4. The numerator becomes 6 times the square root of 3.
5. The denominator becomes the square root of 3 times itself, which is 3.
6. Dividing 6 by 3 leaves 2, so the answer is 2 times the square root of 3.
7. Answering 6 times the square root of 3 forgets to divide by the new denominator.
8. The square root of 18 is the numerator alone with the 6 taken inside the root sign.
_Source: Siyavula Mathematics Grade 11 (Everything Maths, CC BY 4.0), Chapter 1: Exponents and surds_
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