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When you square each side of an equation is the resulting equation equivalent to the original?
Wiki User
∙ 11y ago
For example, x = 2 has only one solution and that is x = 2.
but
x2= 4, the squared equation, has two solutions: x = +2 and x = -2
For example, x = 2 has only one solution and that is x = 2.
but
x2= 4, the squared equation, has two solutions: x = +2 and x = -2
For example, x = 2 has only one solution and that is x = 2.
but
x2= 4, the squared equation, has two solutions: x = +2 and x = -2
For example, x = 2 has only one solution and that is x = 2.
but
x2= 4, the squared equation, has two solutions: x = +2 and x = -2
Wiki User
∙ 11y ago
Wiki User
∙ 11y agoFor example, x = 2 has only one solution and that is x = 2.
but
x2= 4, the squared equation, has two solutions: x = +2 and x = -2
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What is the area of the original square if a square piece of paper is folded in half vertically and the resulting figure has a perimeter of 12 cm?
16 sq cm. Suppose the original square had sides of x cm. Then the folded rectangle has pairs of sides of length x and x/2 cm. The perimeter is 2(x + x/2) = 3x. So 3x = 12 so that x = 4 and the area of the original square, with sides of 4 cm is 16 sq cm.
How do you show square root in a linear equation?
You can't have a square root in a linear equation other than to express a constant. If it is used as such, it is represented the same way as in any other branch of mathematics.
What is 1 square kilometer?
1 square kilometre is an area equivalent to 1 million square metres.
How much is 6500 square feet in meters?
6500 square feet is equivalent to 603.9 square meters
Distance around a triangle?
You can use the Pythagorean Theorem to find the distance around a right triangle. The equation for this is a2 = b2 + c2. Further through the equation, it is a = square root of b2 +c2. If you know one side of the right triangle is 4 and a second side is 6, the equation would be as follows. a2 = b2 + c2 a = square root of 42 + 62 a = square root of 16 + 36 a = square root of 52 a = 7.211
When both sides of the equation are squared the resulting equation is?
Remains true. But this does not apply to square roots.
What is the extraneous solution to w equals sqrt 7w?
An "extraneous solution" is not a characteristic of an equation, but has to do with the methods used to solve it. Typically, if you square both sides of the equation, and solve the resulting equation, you might get additional solutions that are not part of the original equation. Just do this, and check each of the solutions, whether it satisfies the original equation. If one of them doesn't, it is an "extraneous" solution introduced by the squaring.
Do you need to put a plus or minus sign in front of a square root answer you get from finding the inverse of a quadratic equation?
Yes. Quite often, if you don't, you'll lose solutions. That is, the transformed equation - after taking square roots - will have less solutions than the original equation.
When solving a radical equation you should first isolate the radical and then?
It often helps to square both sides of the equation (or raise to some other power, such as to the power 3, if it's a cubic root).Please note that doing this may introduce additional solutions, which are not part of the original equation. When you square an equation (or raise it to some other power), you need to check whether any solutions you eventually get are also solutions of the original equation.
If one side of a square is increased by 4 inches and a adjacent side is multiplied by 4 the perimeter of the resulting rectangle is 3 times the perimeter of the square what is the side of the original?
10d+8=12d the origian square is 4x4
In general when solving a radical equation should you first isolate the radical and then both sides?
It often helps to isolate the radical, and then square both sides. Beware of extraneous solutions - the new equation may have solutions that are not part of the solutions of the original equation, so you definitely need to check any purported solutions with the original equation.
How do you square both sides of a square root equation?
Easy. Say I was going to do ____ \/ 2 =1.41.... So then you square the left side 2=1.41.... And then you square the other side 2=2 (When you square root a number and you square it, you end up with the original number)
What is the height of a triangle with an area 99 square feet and a base of 33 feet?
The idea is to use the equation for the area of a triangle, replace the variables you know (in this case, area and base), and solve the resulting equation for that which you don't know (in this case, the height).
What is the contribution of brahmagupta in quadratic equation?
Brahmagupta gave the solution of the general linear equation in chapter eighteen of Brahmasphutasiddhanta,18.43 The difference between rupas, when inverted and divided by the difference of the unknowns, is the unknown in the equation. The rupas are [subtracted on the side] below that from which the square and the unknown are to be subtracted.[4]Which is a solution equivalent to , where rupasrepresents constants. He further gave two equivalent solutions to the general quadratic equation,18.44. Diminish by the middle [number] the square-root of the rupas multiplied by four times the square and increased by the square of the middle [number]; divide the remainder by twice the square. [The result is] the middle [number].18.45. Whatever is the square-root of the rupasmultiplied by the square [and] increased by the square of half the unknown, diminish that by half the unknown [and] divide [the remainder] by its square. [The result is] the unknown.[4]Which are, respectively, solutions equivalent to,andHe went on to solve systems of simultaneous indeterminate equations stating that the desired variable must first be isolated, and then the equation must be divided by the desired variable's coefficient
What is the square root of 4046.82?
According to my calculator: 63.61462096 it might help if you give the original equation (unless you are looking for huge decimal answers)
Why is it necessary to check for extraneous solutions in radical equations?
1) When solving radical equations, it is often convenient to square both sides of the equation. 2) When doing this, extraneous solutions may be introduced - the new equation may have solutions that are not solutions of the original equation. Here is a simple example (without radicals): The equation x = 5 has exactly one solution (if you replace x with 5, the equation is true, for other values, it isn't). If you square both sides, you get: x2 = 25 which also has the solution x = 5. However, it also has the extraneous solution x = -5, which is not a solution to the original equation.
How do you complete a square math problem?
It often helps to take square roots on both sides of the equation. However, solutions to the original equation may be lost - it is often convenient to put a "plus or minus" sign so as not to lose solutions. Example: x2 = 25 Taking square roots: x = "plus or minus" 5
