Square Roots

You just bought yourself a new poster for your bedroom that has an area of six thousand four hundred centimeters squared. The poster is in the shape of a square, and you must find the side lengths to see where it will fit on your wall before hanging. We can learn more about 'square roots' to determine the dimensions of the square-shaped poster. The square root of a number is a value that, when multiplied by itself, gives the original number. This is a radical sign, the symbol used for the square root function. The term under the radical sign is called a radicand. We can read this as the square root of p, which is defined to mean the positive solution to the equation x squared equals p. Let's now try to find the square root of nine. To solve this, we must think, what multiplied by itself is nine? Three times itself is nine. So the square root of nine equals three. If a radical sign is used like it is in this question, only a positive square root needs to be found, which is also known as the principal square root. However, there is another integer that, when multiplied by itself, equals nine, and that is negative three. Both negative and positive three are the square roots of nine, but because the square root function only gives us the positive solution we can use a plus or minus symbol to show the two roots. Let's look at a problem and solve for the missing variable. Remember x squared means x times x. To find the value of x we will find the square root of both sides. There are two solutions nine, and negative nine because if we square these values, they both result in eighty one. A 'perfect square' is a number that can be expressed as the product of an integer multiplied by itself. For example, the numbers nine and eighty-one are both perfect squares since they have integer roots. Let's see if we can find the square root of twenty. As much as you try, there is not a single integer that multiplies by itself to equal twenty, so this is not a perfect square. To solve for x we can use a calculator to find the square root, which would be this irrational number, and don't forget both the positive and negative square root are solutions. Let's look back at the poster you got for your bedroom. The size listed is six thousand four hundred centimeters squared, but we need to find the dimensions. To find the dimensions of the square poster, we can find the square root of the area, since the area of a square is its side length multiplied by itself. It turns out this number is a perfect square, can you think of what number squared is equal to six-thousand four hundred? We already know that eight squared is sixty-four, if we add a zero to each eight and multiply eighty times eighty, we will arrive at six-thousand four hundred. The solution is plus or minus eighty. However, since we are representing distance, we will not need the negative root, therefore the dimensions of the poster are eighty centimeters by eighty centimeters! Let's recap what we have learned about square roots. A square root is a value that, when multiplied by itself, gives the original number. Every positive number has a square root, but only specific positive numbers are perfect squares. This only happens when an integer is multiplied by itself. The understanding of square roots is important when the goal is to find the dimensions of a square or the missing side of a right triangle. Let's see how that poster fits on your wall!