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Chapter 8: Problem 33

Simplify the squares and square roots. $$6^{2}$$

Short Answer

Expert verified
36

Step by step solution

01

Identify the Power

Recognize that the given expression is in the form of a power: \(6^2\)
02

Calculate the Power

Compute the square of 6 by multiplying it by itself: \(6^2 = 6 \times 6\)
03

Simplify the Result

Multiply 6 by itself: \(6 \times 6 = 36\)

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Simplifying Powers and Exponents
Powers and exponents are fundamental concepts in mathematics that allow us to express repeated multiplication in a simplified way. For example, the expression \(6^2\) involves squaring the number 6. The exponent here is 2, which tells us how many times we need to multiply the base number (6) by itself.

When we encounter a power like \(6^2\), we can break it down into a multiplication problem. This problem means we need to do:
  • \(6 \times 6\)

The exponent (2) tells us the number of times to use the base (6). Here, it results in multiplying 6 by itself, giving us 36. This is the simplified result of the exponentiation.
Understanding Multiplication
Multiplication is a mathematical operation that combines groups of equal sizes. It鈥檚 essentially repeated addition. For example, multiplying 6 by another 6 is the same as adding 6 to itself. When we say \(6 \times 6\), we're saying:
  • \(6 + 6 + 6 + 6 + 6 + 6 = 36\)

Multiplication and exponents are closely related because exponents represent repeated multiplication of the same number. In our case, \(6^2\) means multiplying 6 by itself one time.
Simplifying Square Roots
Square roots are the opposite operation of squaring a number. They ask the question: 'What number, when multiplied by itself, will give the original number?' For example, the square root of 36 is written as \( \sqrt{36} \) and it equals 6 because:
  • \(6 \times 6 = 36\)

Simplifying square roots means finding this original number. When dealing with larger numbers or variables, understanding how to simplify square roots can help solve equations efficiently.

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