Vivian Quach

12/2/2025

Algebra 1

Division and Square Roots

Subjects

Algebra 1

Exponents & Radicals

Radicals

Square Root of Decimal

209

•

Dec 2, 2025

•

2 pages

Understanding Division and Square Roots

Vivian Quach

@vivianquach_wzmx

Mastering how to divide real numbers and calculate square roots... Show more

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Dividing Real Numbers

Ever wonder how division actually works? It's all about using the multiplicative inverse (or reciprocal) of a number. For any non-zero number, its reciprocal is written as $\frac{1}{a}$ . When you multiply a number by its reciprocal, you always get 1.

When dividing numbers, you're actually multiplying by the reciprocal. So $a \div b$ is the same as $a \cdot \frac{1}{b}$ . For example, when you calculate $5 \div 2$ , you're really finding $5 \cdot \frac{1}{2}$ , which equals 2.5.

The sign of your answer depends on the signs of the numbers you're dividing. When dividing two numbers with the same sign (both positive or both negative), your answer is positive. When dividing numbers with different signs, your answer is negative. And remember, when you divide 0 by any non-zero number, the result is always 0.

Remember This: Zero never has a multiplicative inverse because there's no number that can be multiplied by 0 to get 1. This is why dividing by zero is undefined!

Square Roots

Square roots are numbers that, when multiplied by themselves, give you a specific value. If $b^2 = a$ , then b is a square root of a. For example, both 3 and -3 are square roots of 9 because $3^2 = 9$ and $(-3)^2 = 9$ .

Every positive number has two square roots – a positive (principal) square root and a negative square root. We write the positive square root using the radical symbol $\sqrt{}$ . The number under the radical is called the radicand. When we want to refer to both positive and negative square roots, we use the ± symbol.

Perfect squares make working with square roots easier. These are numbers that are the result of squaring an integer. Examples include 1, 4, 9, 25, and 36. When you take the square root of a perfect square, you get an integer.

Math Hack: To quickly identify perfect squares, memorize the first few squared integers: $1^2=1$ , $2^2=4$ , $3^2=9$ , $4^2=16$ , $5^2=25$ , $6^2=36$ . This will make calculating square roots much faster!

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Subjects

Algebra 1

Exponents & Radicals

Radicals

Square Root of Decimal

Algebra 1

•

209

•

Dec 2, 2025

•

2 pages

Understanding Division and Square Roots

Vivian Quach

@vivianquach_wzmx

Mastering how to divide real numbers and calculate square roots is essential for your math success. These operations form the building blocks for more advanced math concepts you'll encounter in high school and beyond.

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Dividing Real Numbers

Remember This: Zero never has a multiplicative inverse because there's no number that can be multiplied by 0 to get 1. This is why dividing by zero is undefined!

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Access to all documents

Improve your grades

Join milions of students

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Square Roots

Math Hack: To quickly identify perfect squares, memorize the first few squared integers: $1^2=1$ , $2^2=4$ , $3^2=9$ , $4^2=16$ , $5^2=25$ , $6^2=36$ . This will make calculating square roots much faster!