When is square root plus and minus

When two same square roots are multiplied, then the result must be a radical number. It shows that the result is a non-square root number. The square root of negative numbers is undefined. Hence the perfect square cannot be negative.

Some of the numbers end with 2, 3, 7, or 8 in the unit digit , then the perfect square root does not exist. Some of the numbers end with 1, 4, 5, 6, or 9 in the unit digit, then the number will have a square root.

It is easy to find the square root of a number that is a perfect square. Perfect squares are those positive numbers that can be written as the multiplication of a number by itself, or you can say that a perfect square is a number which is the value of power 2 of any integer. The number that can be expressed as the product of two equal integers.

However, 24 is not a perfect square because it cannot be expressed as the product of two equal integers. The number which is obtained by squaring a whole number is termed as a perfect square. Here, 81 is a perfect square of 9 because it is the square of a whole number. If the square root is a whole number then the given number will be a perfect square, and if the square root value is not a whole number, then the given number is not a perfect square. For instance, to check whether 24 is a perfect square or not, we will calculate its square root.

As we can see, 4. We can see that 7 is a whole number, therefore, 49 is a perfect square. Why do we use plus or minus in square root? The numbers that are not a perfect square are members of the irrational numbers.

Sample Problems Question 1: What are the two square roots of ? Skip to content. Change Language. Related Articles.

This can be converted into a difference of squares, as long as we allow the square root of seven to be one of the values being squared:. When we take the square root of either side, we get the following:. The technical definition of "the square root of x squared" is "the absolute value of x ".

That is:. Because of this highly technical consideration, the equation actually simplifies as:. But x could be positive or negative though not zero, obviously.

To solve this absolute-value equation , we must consider each of the two cases. If x is positive, then we can remove the absolute-value bars without changing anything:. On the other hand, if x is negative, then we must change the sign on x when we remove the absolute-value bars, so we get:. If the radicand is not a perfect square i. The square roots of numbers that are not a perfect square are members of the irrational numbers. This means that they can't be written as the quotient of two integers.

The decimal form of an irrational number will neither terminate nor repeat. The irrational numbers together with the rational numbers constitutes the real numbers.

Video lesson Approximate the square root of More classes on this subject Algebra 1 Exploring real numbers: Integers and rational numbers Algebra 1 Exploring real numbers: Calculating with real numbers Algebra 1 Exploring real numbers: The Distributive property. Search Math Playground All courses.