Simplify. (7)/(4-√(3))

Name: Problem 46, Chapter 7: Algebra 2
Uploaded: 2020-03-18T17:37:01-08:00
Duration: 2 min 31 s
Channel: Emily Schilz
Description: Simplify. (7)/(4-√(3))

step 1 For this expression, in order to simplify, we need to make sure that there are no radicals left

Question

Simplify. $\frac{7}{4-\sqrt{3}}$

   Simplify.
$\frac{7}{4-\sqrt{3}}$

Algebra 2

Holliday, Luchin,… 1st Edition

Chapter 7, Problem 46

Instant Answer

Solved by Expert Emily Schilz

03/18/2020

Step 1

\[ \frac{7}{4-\sqrt{3}} \times \frac{4+\sqrt{3}}{4+\sqrt{3}} \] Show more…

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Simplify. $\frac{7}{4-\sqrt{3}}$

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Key Concepts

Rationalization of the Denominator

This is a technique used to remove irrational elements, such as square roots, from the denominator of a fraction. By multiplying the numerator and denominator by a suitable expression, one can transform the denominator into a rational number, which often simplifies the expression and makes further arithmetic operations easier.

Conjugate

The conjugate of a binomial expression that contains a radical, such as a - ?b, is the expression a + ?b. Multiplying by the conjugate leverages the difference of squares formula, which helps eliminate the radical in the denominator when simplifying fractions.

Difference of Squares

This algebraic formula, expressed as (a - b)(a + b) = a^2 - b^2, is essential in simplifying products involving conjugates. It allows the direct removal of square roots from the denominator by converting the product into the difference of two squares, typically resulting in a rational number.

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