Find the square root: √361 Select the correct choice below and, if necessary, fill in the answer box within your choice. A. The square root is __. B. The square root is not a real number.
The Correct Answer and Explanation is:
Correct Choice: A. The square root is 19.
Explanation:
The square root of a number is a value that, when multiplied by itself, gives the original number. In mathematical terms:x=y if and only if y×y=x\sqrt{x} = y \text{ if and only if } y \times y = xx=y if and only if y×y=x
In this case, we are asked to find:361\sqrt{361}361
We want to determine which number multiplied by itself equals 361. Let’s try a few possibilities:
- 18×18=32418 \times 18 = 32418×18=324
- 19×19=36119 \times 19 = 36119×19=361
Since 19×19=36119 \times 19 = 36119×19=361, we conclude:361=19\sqrt{361} = 19361=19
Therefore, 19 is the principal (positive) square root of 361. Square roots of perfect squares like this one are always rational numbers if the number inside the square root is a perfect square. A perfect square is a number that can be expressed as the product of an integer with itself.
Some examples of perfect squares include:
- 12=11^2 = 112=1
- 22=42^2 = 422=4
- 32=93^2 = 932=9
- 102=10010^2 = 100102=100
- 202=40020^2 = 400202=400
Similarly, since 361 is equal to 19219^2192, it is a perfect square.
Also, 361 is a positive number, so its square root must be a real number. That eliminates option B, which says the square root is not a real number.
To summarize:
- The square root of 361 is a whole number
- It is a real, rational number
- The correct answer is A. The square root is 19
