Which option is the simplified form of √128?
Answer and explanation
Correct answer: 8√2
To simplify a square root, factor the radicand into the greatest possible perfect square multiplied by a remaining factor. Since 128 = 64 × 2 and √64 = 8, we get √128 = √(64 × 2) = √64 × √2 = 8√2. Option B is too large because (16√2)² = 512, not 128. Options C and D are mathematically equal to √128 before complete simplification, because 4√8 = 8√2 and 2√32 = 8√2, but they still contain a square factor inside the radical and are not in simplest form. Thus the fully simplified answer is option A.
Frequently asked questions
What is the correct answer to this question?
8√2
Why is this the correct answer?
To simplify a square root, factor the radicand into the greatest possible perfect square multiplied by a remaining factor. Since 128 = 64 × 2 and √64 = 8, we get √128 = √(64 × 2) = √64 × √2 = 8√2. Option B is too large because (16√2)² = 512, not 128. Options C and D are mathematically equal to √128 before complete simplification, because 4√8 = 8√2 and 2√32 = 8√2, but they still contain a square factor inside the radical and are not in simplest form. Thus the fully simplified answer is option A.
Which subject and chapter does this question cover?
This is a Class 10 Mathematics question. Chapter: Polynomials. Topic: Irrational numbers and real numbers.
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