# Solve by using square roots

Square roots are useful for solving simple equations when the numbers involved are relatively simple. For example, if you want to find the square root of 694, you can simply multiply both sides of the equation by itself: 1 694 = (1) 694 + (1) 694 = 1 + 9 = 10 Square roots simplify many other problems as well. For example, if you are trying to figure out how many gallons of water it takes to fill a swimming pool 12 inches deep, you can use square roots to calculate the answer.

## Solving by using square roots

First, convert feet to meters: 12 feet = 1 meter. Then, multiply both sides of the equation by 2: (12) meters * 2 = 36 meters Now, divide both sides by 36: (12/36) * 12 = 4.5 gallons For other types of problems where square roots can help, see below.

Solving a quadratic equation by using square roots is one of the most common ways to solve a quadratic equation. To find the solution to a quadratic equation, you can use the formula: To solve for x, set the equation equal to zero by dividing both sides by 2 on one side and then subtracting . The result is the value of x that satisfies the given quadratic equation. If you get 0, then x must be 0; if you get 1, then x must be 1; and so on. Square roots are also used in other types of equations, including linear and exponential equations. For example, if you are solving an exponential equation like y = 3x + 5, you could square both sides of the equation to solve for x or take the square root of both sides to solve for y (y = 3√5). If you're uncertain about whether your answer should be positive or negative, it's usually safer to round down. This will ensure that your answer will always be between -1 and +1. But if you have a method for determining whether two values are particularly close together, it's okay to round up. For example, if you're only one decimal place away from being exactly between 4.8 and 5.0 on a scale of 1-10, it's acceptable to round up to 5

Square roots are used to solve equations that are expressed in numbers where the number is not an integer. To use the square root of a number, add the square of the number to the other side of the equation. For example, if you have 3 + 4 = 7 and you want to simplify it, you would use: 3 + 4 = 7 x 2, or 3 + 4 = 7 x 2. To find the square root of a number, divide the number by itself. For example: Since negative numbers cannot be squared, we must first subtract 1 from them before squaring them. So if we have −8 −4 −1, then: Therefore −4 = −8 -3 −1. The answer is in fact -1 because this is an even number, so we can take its square root to find that it is also even. We can therefore conclude that 1 is an even number and so it must also be a square root for any given positive or negative integer value. The rules above apply to all numbers but one: rational numbers (numbers with a decimal point). Unlike real numbers (those without decimal points), rational numbers can be both integers and fractions. If a fraction is solved using a formula such as “left divided by right”, then the result will be a rational number. Fractions with denominators greater than