Answer :
To determine which definition best describes the term "square root," let's analyze each option provided:
a. "Is the 'fraction part' (part after the decimal). For example, the mantissa of the number 12.345 is .345."
- This definition describes the mantissa, not the square root. The mantissa is the decimal part of a logarithm or a number, which is unrelated to the concept of a square root.
b. "A value when multiplied by itself gives the number."
- This is the correct definition of a square root. For example, the square root of 4 is 2 because \(2 \times 2 = 4\).
c. "The result of multiplying a number by itself."
- This defines a 'square,' not a square root. For instance, the square of 3 is 9, which is the result of \(3 \times 3\).
d. "Any number that can be made by dividing one integer by another. The word comes from 'ratio.'"
- This definition refers to a rational number, which is a number that can be expressed as a fraction where both the numerator and the denominator are integers.
After evaluating all the options:
- Option a is incorrect because it describes the mantissa.
- Option c is incorrect because it defines a square.
- Option d is incorrect because it explains a rational number.
Hence, the best definition of "square root" is given by option b, which states that a square root is a value that, when multiplied by itself, gives the original number.
a. "Is the 'fraction part' (part after the decimal). For example, the mantissa of the number 12.345 is .345."
- This definition describes the mantissa, not the square root. The mantissa is the decimal part of a logarithm or a number, which is unrelated to the concept of a square root.
b. "A value when multiplied by itself gives the number."
- This is the correct definition of a square root. For example, the square root of 4 is 2 because \(2 \times 2 = 4\).
c. "The result of multiplying a number by itself."
- This defines a 'square,' not a square root. For instance, the square of 3 is 9, which is the result of \(3 \times 3\).
d. "Any number that can be made by dividing one integer by another. The word comes from 'ratio.'"
- This definition refers to a rational number, which is a number that can be expressed as a fraction where both the numerator and the denominator are integers.
After evaluating all the options:
- Option a is incorrect because it describes the mantissa.
- Option c is incorrect because it defines a square.
- Option d is incorrect because it explains a rational number.
Hence, the best definition of "square root" is given by option b, which states that a square root is a value that, when multiplied by itself, gives the original number.
