The square root of 15 is not a rational number. It is an irrational number. Here's why. A rational number is a number that can be expressed in the form of p/q, where p, q ∈ Z and q ≠ 0. A number is irrational if it is non-terminating with no repeating patterns in its decimal part. Now let us look at the square root of 15, the decimal representation of √15 is 3.87298334621... Do you think the decimal part stops after 3.87298334621...? No, it is never-ending. It is a non-terminating decimal with non-repeating digits. The number 2.15215427125... can't be written in p/q form, where p and q are integers. So, the square root of 15 is not a rational number. It is an irrational number.
How to Find the Square Root of 15?
We will discuss two methods of finding the square root of 15. Express the radicand to be the product involving perfect square(s) and simplifying it
Long division method for perfect and non-perfect squares. Let's discuss the first method, Simplifying a square root means to rewrite it in such a way that there are no perfect squares left in the radicand. √50 can be simplified to 5√2 but √15 cannot be simplified further. Let us learn the reason behind. The prime factorization of 15 is 15 = 3 × 5. For simplifying √15 further we will need one or more pairs of the same factors. Such pairs of factors are not available. Therefore, √15 cannot be simplified further.
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The square root of 15 is not a rational number. It is an irrational number. Here's why. A rational number is a number that can be expressed in the form of p/q, where p, q ∈ Z and q ≠ 0. A number is irrational if it is non-terminating with no repeating patterns in its decimal part. Now let us look at the square root of 15, the decimal representation of √15 is 3.87298334621... Do you think the decimal part stops after 3.87298334621...? No, it is never-ending. It is a non-terminating decimal with non-repeating digits. The number 2.15215427125... can't be written in p/q form, where p and q are integers. So, the square root of 15 is not a rational number. It is an irrational number.
How to Find the Square Root of 15?
We will discuss two methods of finding the square root of 15. Express the radicand to be the product involving perfect square(s) and simplifying it
Long division method for perfect and non-perfect squares. Let's discuss the first method, Simplifying a square root means to rewrite it in such a way that there are no perfect squares left in the radicand. √50 can be simplified to 5√2 but √15 cannot be simplified further. Let us learn the reason behind. The prime factorization of 15 is 15 = 3 × 5. For simplifying √15 further we will need one or more pairs of the same factors. Such pairs of factors are not available. Therefore, √15 cannot be simplified further.
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The numbers lying between the square of 15 and 16 are
226,227,228,229,230,231,232,233,234,235,236,237,238,239,240,241,242,243,244,245,246,247,248,249,250, 251,252,253,254,255,256.
The total no of numbers are 31.