What number squared equals 1.5?
The Correct Answer and Explanation is :
To find the number that squared equals 1.5, we can set up the equation:
[
x^2 = 1.5
]
To solve for (x), we take the square root of both sides:
[
x = \sqrt{1.5}
]
Calculating the square root of 1.5 gives us approximately:
[
x \approx 1.2247
]
This means that both (1.2247) and (-1.2247) are solutions, since squaring either of these numbers will yield (1.5).
Explanation
The operation of squaring a number involves multiplying the number by itself. For instance, if we take the number (x) and square it, the result is (x^2). In this case, we are trying to find a number whose square is (1.5). The equation (x^2 = 1.5) indicates that (x) can be positive or negative since squaring either a positive or a negative number yields a positive result.
The square root function is the inverse of the squaring function. Therefore, to find the square root of (1.5), we determine what value, when multiplied by itself, gives us (1.5). This is where the positive and negative roots come into play: mathematically, the square root of a positive number (a) produces two solutions: (\sqrt{a}) and (-\sqrt{a}).
Calculators or software can be used to compute the square root directly, but understanding the fundamental principles behind squaring and square roots is essential. The value (\sqrt{1.5}) can be approximated by recognizing that (1.5) is between (1) (where the square root is (1)) and (4) (where the square root is (2)).
Thus, the number (x) such that (x^2 = 1.5) is approximately (1.2247) or (-1.2247).