Question

Simplify and reduce each expression. $$\frac{-10 \pm \sqrt{75}}{10}$$

Name: Problem 7, Chapter 6: Intermediate Algebra
Uploaded: 2022-03-02T23:06:54-08:00
Duration: 23 s
Channel: Victor Salazar
Description: Simplify and reduce each expression. (-10 ±√(75))/(10)

   Simplify and reduce each expression.
$$\frac{-10 \pm \sqrt{75}}{10}$$

Intermediate Algebra

Jerome E. Kaufmann,… 10th Edition

Chapter 6, Problem 7

Instant Answer

Solved by Expert Victor Salazar

03/02/2022

Step 1

The square root of 75 can be simplified to 5 times the square root of 3, because 75 is 25 times 3 and the square root of 25 is 5. So, we have: $$\frac{-10 \pm \sqrt{75}}{10} = \frac{-10 \pm 5\sqrt{3}}{10}$$ Show more…

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Simplify and reduce each expression. $$\frac{-10 \pm \sqrt{75}}{10}$$

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Key Concepts

Understanding the Plus-Minus Operator

The plus-minus (±) symbol indicates that the expression encompasses two distinct cases: one where the term is added and one where it is subtracted. This is important when dealing with expressions involving radicals, as it captures both potential values of the expression.

Simplifying Radical Expressions

This involves expressing a square root in its simplest form by identifying and extracting perfect square factors from the radicand. In general, if the radicand can be factored into a perfect square and another factor, the square root of the perfect square is taken outside the radical, simplifying the expression.

Simplifying Rational Expressions

This concept focuses on reducing fractions by canceling any common factors between the numerator and the denominator. It ensures that the expression is represented in its reduced or simplest form, making it easier to interpret and further manipulate if needed.

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