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Without a calculator, between which two consecutive whole numbers does the square root of 30 lie?
A5 and 6
B4 and 5
C6 and 7
D3 and 4
Answer & Solution
Correct answer: A. 5 and 6
1. A surd can be placed on the number line using the perfect squares around it.
2. A perfect square is the number you get when an integer is squared.
3. The perfect square just below 30 is 25, since 5 times 5 is 25.
4. The perfect square just above 30 is 36, since 6 times 6 is 36.
5. So 30 lies between 25 and 36.
6. Taking square roots keeps that order, so the square root of 30 lies between 5 and 6.
7. Choosing 6 and 7 would mean the number lies between 36 and 49, which is too high.
_Source: Siyavula Mathematics Grade 10 (Everything Maths, CC BY 4.0), Chapter 1: Algebraic expressions_
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