What are the square roots of 4 and 49
The Correct Answer and Explanation is:
The square roots of 4 and 49 are 2 and 7, respectively.
Explanation:
The square root of a number is a value that, when multiplied by itself, gives the original number. Mathematically, the square root of a number n is represented as √n.
- Square root of 4: The square root of 4 is the number that, when multiplied by itself, equals 4.
- 4=2\sqrt{4} = 24=2, because 2×2=42 \times 2 = 42×2=4.
- Another way to think about this is that 4 can be written as 222^222, so the square root of 4 is just 2.
- Square root of 49: The square root of 49 is the number that, when multiplied by itself, equals 49.
- 49=7\sqrt{49} = 749=7, because 7×7=497 \times 7 = 497×7=49.
- You could also express 49 as 727^272, which directly shows that the square root of 49 is 7.
In both cases, we’re looking for a number that can “reverse” the effect of squaring (multiplying a number by itself). The square root is always a non-negative number, and in these examples, both 2 and 7 are positive. For any positive number nnn, the square root will be positive, but there is also a negative square root. In this case, the negative square roots of 4 and 49 are -2 and -7, respectively, but we usually refer to the principal (positive) square root unless specified otherwise.
This property of square roots is important in many areas of mathematics, including algebra, geometry, and calculus, as it helps simplify equations and solve for unknowns.
