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Written in simplest surd form, the square root of 50 becomes which expression?
A2 times the square root of 5
B10 times the square root of 5
C25 times the square root of 2
D5 times the square root of 2
Answer & Solution
Correct answer: D. 5 times the square root of 2
1. A surd is simplified by writing its radicand as a product of factors.
2. Look for a factor of 50 that is a perfect square.
3. 50 can be written as 25 times 2, and 25 is a perfect square.
4. The square root of 25 is 5, so that factor comes out of the root sign.
5. The square root of 50 is therefore 5 times the square root of 2.
6. Answering 25 times the square root of 2 forgets to take the root of the perfect square.
_Source: Siyavula Mathematics Grade 11 (Everything Maths, CC BY 4.0), Chapter 1: Exponents and surds_
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