Question

Evaluate each expression. $$6+3 \sqrt{6^{2}+2 \cdot 2^{5}}$$

   Evaluate each expression.
$$6+3 \sqrt{6^{2}+2 \cdot 2^{5}}$$

Algebra for College Students

Algebra for College Students

Mark Dugopolski 5th Edition

Chapter 1, Problem 48

Instant Answer

Solved by Expert Amy Jiang

04/25/2020

Step 1

We have $6^{2}$ and $2 \cdot 2^{5}$. We calculate these as $6^{2} = 36$ and $2 \cdot 2^{5} = 64$. Show more…

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Evaluate each expression. $$6+3 \sqrt{6^{2}+2 \cdot 2^{5}}$$

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Key Concepts

Order of Operations

This concept dictates the sequence in which parts of a mathematical expression should be evaluated, typically following the PEMDAS/BODMAS rules. It ensures that exponents and operations within grouping symbols are handled before multiplication, division, addition, or subtraction, thereby yielding a consistent result.

Exponentiation

Exponentiation involves raising a number to a particular power, signifying repeated multiplication of the number by itself. This concept is fundamental in simplifying expressions where numbers are presented as powers.

Radical Expressions

Radical expressions involve the use of roots, such as square roots, which represent a value that, when multiplied by itself a certain number of times, gives the original number. Simplifying radical expressions often requires evaluating the radicand first (inside the radical) and then determining the simplest form of the root.

Arithmetic Operations

Arithmetic operations include addition, subtraction, multiplication, and division. Mastery of these operations, especially in combination with the order of operations, is essential for accurately evaluating and simplifying mathematical expressions.

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