Question

I am looking for the EXACT answer. Not what two square numbers It is between. Not a part of the irrational number it is. I want the EXACT answer which means you need to think of how we write the square root of non-perfect square numbers. You can write square root by copying and pasting this symbol -> V < or by writing square root (number) or sqrt(number) b2 = 77

Answer 1

The exact answer for the square root of a non-perfect square number, such as when b2 equals 77, is expressed in radical form as √77 or 77^(1/2), representing the positive root of the number 77.

Step-by-step explanation:

When dealing with the sqrt(b2) where b2 equals 77, we are working with a square root of a non-perfect square number. The exact value cannot be expressed as a simple integer or a fraction because 77 is not a perfect square. However, in mathematics, we represent the square root of non-perfect squares in radical form, maintaining the integrity of the number without approximation.

Using the properties of exponents and square roots, we interpret the square root of an expression as that expression raised to the power of 1/2. Therefore, the square root of b2 when b2 is equal to 77 is represented as 77^(1/2) or √77. This representation is exact and implies the positive root of the number 77.

In a calculation or when entering this value into a calculator, it is essential to use the square root function to work with this irrational number precisely. Remember, a number such as √77 cannot be simplified to a precise decimal or fraction, but we can use this radical form to perform algebraic manipulations exactly without approximations.