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Chapter 10: Problem 45

Use mental math to find the product. $$16^{2}$$

Short Answer

Expert verified
The square of 16 is 256.

Step by step solution

01

Understand the given exercise

Here, the number 16 is to be squared, which means we have to multiply the number 16 by itself.
02

Multiply the number by itself

To perform this operation mentally, think of 16 times 16. The multiplication gives us the result: \(16*16 = 256\).
03

Conclusion.

Using basic math skills, we find that the square of number 16 is 256.

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Key Concepts

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

Squaring Numbers
Squaring a number essentially means multiplying the number by itself. If you are asked to find the square of 16, you are tasked with calculating what 16 times 16 equals.
\[16^2 = 16 \times 16\]
This operation may seem daunting at first, but once understood, it becomes a fundamental part of mathematics.

When you square a number, you're expanding it to understand a larger perspective of its value. For instance:
  • 16 means you've counted up to 16 once.
  • 16 squared, 16 x 16, is like you're expanding this count 16 times.
In mental math, it helps to break down numbers into friendlier parts (like thinking of 16 as 10 + 6) to simplify calculations.
Basic Multiplication
Basic multiplication is all about understanding how to combine numbers to get products. It's one of the first mathematical skills learned and is useful throughout all levels of math.

Multiplication can be viewed as repeated addition. Instead of adding 16 together 16 times, multiplication allows us to efficiently compute the same result.
For example:
  • 16 times 16 is the same as adding the number 16, 16 times.

Using mental math for multiplication may seem overwhelming, but with practice, it becomes natural. A useful method for mental multiplication is to break numbers down into more manageable portions, solve them, and then combine results together at the end.
Arithmetic Skills
Arithmetic skills are the basic numerical skills that serve as the foundation for more complex mathematics. They include addition, subtraction, multiplication, and division.

Mental math enhances these skills by teaching efficient calculation methods without always relying on paper or calculators.
When honing arithmetic skills, try:
  • Practicing mental calculations regularly.
  • Breaking numbers into smaller components, like turning 16 into 10 and 6, to simplify operations.
  • Memorizing multiplication tables for quicker recall.

Improving arithmetic skills builds confidence in handling numbers, which can promote better understanding and proficiency in more advanced mathematical concepts.

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Most popular questions from this chapter

Find the product. $$(11-6 x)^{2}$$

Use factoring to solve the equation. Use a graphing calculator to check your solution if you wish. $$3 x^{2}-24 x+48=0$$

In Exercises \(69-72,\) you are tutoring a friend and want to create some quadratic equations that can be solved by factoring. Find a quadratic equation that has the given solutions and explain the procedure you used to obtain the equation. $$-\frac{1}{2}\( and \)\frac{1}{3}$$

Use a is calculator to evaluate the expression. Round the result to two decimal places when appropriate. $$(1.1 \cdot 3.3)^{3}$$

Which one of the following is a correct factorization of the expression \(-16 x^{2}+36 x+52 ?\). A) \((-16 x+26)(x-2)\) (B) \((-4 x-13)(4 x+4)\) (C) \(-1(4 x-13)(4 x+4)\) (D) \(-1(4 x-4)(4 x+13)\)
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