Question

Determine the exact answer in simplified form. $$ 45-\sqrt{ } $$

   Determine the exact answer in simplified form.
$$
45-\sqrt{ }
$$

Elementary Algebra

Elementary Algebra

John Redden 1st Edition

Chapter 1, Problem 57

Instant Answer

Solved by Expert James Kiss

01/22/2022

Step 1

So, we can rewrite $\sqrt{45}$ as $\sqrt{9 \times 5}$. Show more…

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Determine the exact answer in simplified form. $$ 45-\sqrt{ } $$

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Key Concepts

Exact Values Versus Approximations

In many mathematics problems, especially those involving radicals, it is important to represent the answer exactly rather than as a decimal approximation. This concept stresses keeping an expression in its most precise and simplified algebraic form, ensuring that all irrational components are maintained as simplified surds for accurate evaluation and further manipulation.

Simplification of Radical Expressions

This concept involves rewriting expressions containing radicals in a form that cannot be simplified any further. It typically requires factorizing the number under the radical sign to extract perfect square factors, thereby rewriting the square root as the product of an integer and a simplified radical. This process is essential for expressing answers exactly, without resorting to decimal approximations.

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