The Square Root Of 17 Simplified: Explanation And Solution

Square Root of 17 How to Find the Square Root of 17? from byjus.com

What is a Square Root?

A square root is a mathematical operation that gives the value which, when multiplied by itself, gives the original number. For example, the square root of 16 is 4 because 4 times 4 equals 16. The symbol for square root is √.

What is the Square Root of 17?

The square root of 17 cannot be simplified to an exact whole number because 17 is a prime number. The decimal approximation of the square root of 17 is approximately 4.123.

How to Simplify the Square Root of 17?

Since the square root of 17 cannot be simplified to a whole number, it is often left in radical form as √17. However, there are some ways to simplify expressions involving the square root of 17.

Method 1: Rationalizing the Denominator

If the square root of 17 appears in the denominator of a fraction, it can be simplified by multiplying both the numerator and denominator by the square root of 17. This will eliminate the radical from the denominator. For example, (1/√17) can be simplified as follows: (1/√17) x (√17/√17) = √17/17

Method 2: Using the Pythagorean Theorem

The Pythagorean theorem states that in a right triangle, the sum of the squares of the two shorter sides is equal to the square of the longest side (the hypotenuse). This can be used to simplify expressions involving the square root of 17. For example, if two sides of a right triangle are 4 and √17, the length of the hypotenuse can be found as follows: 4² + (√17)² = h² 16 + 17 = h² 33 = h² h = √33

Conclusion

In conclusion, the square root of 17 cannot be simplified to an exact whole number. However, it can be left in radical form or simplified using methods such as rationalizing the denominator or the Pythagorean theorem. Understanding how to simplify expressions involving the square root of 17 can be useful in various mathematical applications.