Square root of 80 nearest integer
The Correct Answer and Explanation is :
The square root of 80 is approximately 8.944, which, when rounded to the nearest integer, is 9.
Explanation
To understand how to find the square root of 80, we can break it down into smaller parts. The square root of a number ( x ) is a value ( y ) such that when ( y ) is multiplied by itself, it equals ( x ). In mathematical terms, this is expressed as ( y^2 = x ).
The number 80 can be factored into its prime components:
[ 80 = 2^4 \times 5 ]
To find the square root, we can utilize the properties of square roots and break it down:
[ \sqrt{80} = \sqrt{2^4 \times 5} ]
This can be simplified as follows:
[ \sqrt{80} = \sqrt{(2^2)^2 \times 5} = 2^2 \times \sqrt{5} = 4\sqrt{5} ]
Next, we need to estimate the value of ( \sqrt{5} ). The square root of 5 is approximately 2.236. Therefore:
[ 4\sqrt{5} \approx 4 \times 2.236 \approx 8.944 ]
Now, rounding 8.944 to the nearest integer gives us 9.
This approximation can also be visualized on a number line. Since ( 8^2 = 64 ) and ( 9^2 = 81 ), we know that ( \sqrt{80} ) lies between 8 and 9. Specifically, since 8.944 is much closer to 9 than it is to 8, we confirm that the nearest integer is indeed 9.
In summary, the square root of 80 is approximately 8.944, and rounding this value leads us to conclude that the nearest integer is 9. Understanding square roots and their properties allows for simpler calculations and better estimations in mathematics.