is square root of 56 a rational number? explain uranswer using what you know about rational and irrational numbers.
thnx alot!
No, it is not rational.
sqrt(56)=sqrt(4*14)=sqrt(4*2*7)
sqrt2, sqrt 7 are irrational. The only square roots that are rational are squares of rational numbers.
To determine if the square root of 56 is a rational number, we need to understand the concepts of rational and irrational numbers.
A rational number is any number that can be expressed as a fraction (a/b), where a and b are integers and b is not equal to 0. In other words, a rational number can be written as a finite or recurring decimal.
On the other hand, an irrational number is any number that cannot be expressed as a fraction. Irrational numbers have non-recurring, non-terminating decimal expansions. Examples of irrational numbers include √2, √3, and π.
Now let's consider the square root of 56. Using a calculator, we find that the square root of 56 is approximately 7.48331477. This decimal number is not terminating or recurring, indicating that it is an irrational number.
We can further demonstrate that √56 is irrational by showing that it cannot be expressed as a fraction. If it could be represented as a fraction, it should have a simplified form, meaning that the numerator and denominator have no common factors other than 1.
However, when we try to simplify √56, we find that 56 can be factorized into 2 * 2 * 2 * 7. Since there is a square factor (2^2) in the prime factorization of 56, the square root cannot be simplified. This implies that it cannot be expressed as a fraction, making √56 an irrational number.
Therefore, the square root of 56 is an irrational number, not a rational number.