what two numbers does the square root of 46 lies
The correct answer and explanation is:
The square root of 46 lies between the numbers 6 and 7.
To understand this, first recall that the square root of a number is the value that, when multiplied by itself, gives the original number. In this case, we are looking for a number xx such that x2=46x^2 = 46.
To find where the square root of 46 lies, let’s consider the squares of integers near 46:
- 62=366^2 = 36
- 72=497^2 = 49
Since 4646 is between 36 and 49, the square root of 46 must be between 6 and 7. We can narrow this down further by estimating the square root:
- 6.52=42.256.5^2 = 42.25
- 6.82=46.246.8^2 = 46.24
Since 4646 is closer to 46.2446.24, it shows that the square root of 46 is closer to 6.8. However, it is not an integer, and its exact value is approximately 6.782.
Therefore, the square root of 46 is approximately 6.782, and it lies between the whole numbers 6 and 7.