How do you find the approximate and exact solutions for square root of 45
The perfect squares above and below 45 are 36 and 49. The square root of 45 is between 6 and 7.
Use your calculator to find the exact square root.
To find the approximate and exact solutions for the square root of 45, we can use different methods.
1. Approximate Solution:
One way to find an approximate solution is to use a calculator. Most calculators have a square root function that can provide an approximation of the square root of a number. Enter 45 on your calculator and press the square root button to get an approximate value. In this case, the approximate square root of 45 is approximately 6.7082.
2. Exact Solution:
To find the exact solution, we need to factorize 45 in order to simplify the square root expression.
The prime factorization of 45 can be expressed as 3 * 3 * 5.
(Note: We took the square root of 45 and wrote it as a multiplication of primes)
Using this factorization, we can simplify the square root expression:
√45 = √(3 * 3 * 5)
= √(3^2 * 5)
= 3√5
So the exact solution for the square root of 45 is 3√5, where √ represents the square root symbol.
In summary, the approximate solution for the square root of 45 is approximately 6.7082, while the exact solution is 3√5.