Simplify √(7)(√(2)+2).

Name: Problem 66, Chapter 10: Elementary Algebra
Uploaded: 2020-04-14T04:28:52-08:00
Duration: 27 s
Channel: Lily An
Description: Simplify √(7)(√(2)+2).

step 1 So since they already have a common denominator, I'm just going to add straight across. So 2 plu

Question

Simplify $\sqrt{7}(\sqrt{2}+2)$.

   Simplify $\sqrt{7}(\sqrt{2}+2)$.

Elementary Algebra

Wade Ellis, Jr. 1st Edition

Chapter 10, Problem 66

Instant Answer

Solved by Expert Lily An

04/14/2020

Step 1

First, we can distribute the $\sqrt{7}$ to both terms inside the parentheses: $\sqrt{7}(\sqrt{2}+2) = \sqrt{7}\cdot\sqrt{2} + \sqrt{7}\cdot2$ Now, we can simplify the first term by multiplying the square roots: $\sqrt{7}\cdot\sqrt{2} = \sqrt{7\cdot2} = Show more…

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Simplify $\sqrt{7}(\sqrt{2}+2)$.

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Key Concepts

Distributive Property

The distributive property allows one to multiply a term outside the parentheses by each term within the parentheses individually. This property is fundamental in algebra and is especially useful when simplifying expressions that involve radicals, ensuring each term is appropriately handled during multiplication.

Multiplication of Radicals

Multiplication of radicals involves combining the square roots by multiplying their radicands. The basic property ?a * ?b = ?(ab) applies if a and b are non-negative, facilitating the simplification of expressions with multiple radical terms.

Simplifying Radical Expressions

Simplifying radical expressions means rewriting them in a form that has no reducible square factors inside the square root and no radicals in the denominator. This often involves applying the distributive property alongside the multiplication of radicals, as well as combining like terms to express the result in its simplest form.

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