/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 69 Perform the indicated operations... [FREE SOLUTION] | 91Ó°ÊÓ

91Ó°ÊÓ

Perform the indicated operations. Simplify the answer when possible. \(3 \sqrt{7}-5 \sqrt{14} \cdot \sqrt{2}\)

Short Answer

Expert verified
-7 \sqrt{7}

Step by step solution

01

Identify Radical Expression Components

Identify each component in the radical expression. The first term is \(3 \sqrt{7}\) and the second is \(5 \sqrt{14} \cdot \sqrt{2}\).
02

Simplifying the Second Component

Using the principle that \( \sqrt{a} \cdot \sqrt{b} = \sqrt{ab}\), re-write the second part as \(5 \sqrt{14 \cdot 2}\). This simplifies further to \(5 \sqrt{28} = 5 \cdot 2 \sqrt{7} = 10 \sqrt{7}\).
03

Simplifying the Whole Expression

Now combine the first and second terms. So, \(3 \sqrt{7} - 10 \sqrt{7} = -7 \sqrt{7}\).

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