The square root if taken out from a number gives what?
Ex:✓2³ if square root is taken away what will it become?
Answers
Answer:
What you will learn in this lesson
So far you have solved linear equations, which include constant terms—plain numbers—and terms with the variable raised to the first power, x^1=xx
1
=xx, start superscript, 1, end superscript, equals, x.
You will now learn how to solve quadratic equations, which include terms where the variable is raised to the second power, x^2x
2
x, squared.
Here are a few examples of the types of quadratic equations you will learn to solve:
x^2=36x
2
=36x, squared, equals, 36
(x-2)^2=49(x−2)
2
=49left parenthesis, x, minus, 2, right parenthesis, squared, equals, 49 Why is this a quadratic equation?
2x^2+3=1312x
2
+3=1312, x, squared, plus, 3, equals, 131
Now let's get down to business.
Solving x^2=36x
2
=36x, squared, equals, 36 and similar equations
Suppose we want to solve the equation x^2=36x
2
=36x, squared, equals, 36. Let's first verbalize what the equation is asking us to find. It is asking us which number, when multiplied by itself, equals 36.
If this question sounds familiar to you, it's because this is the definition of the square root of 36, which is expressed mathematically as \sqrt{36}
36
square root of, 36, end square root.
Now, this is how the complete solution of the equation looks:
\begin{aligned}x^2&=36\\\\ \sqrt{x^2}&=\sqrt{36}&&\text{Take the square root.}\\\\ x&=\pm\sqrt{36}\\\\ x&=\pm 6\end{aligned}
x
2
x
2
x
x
=36
=
36
=±
36
=±6
Take the square root.
Let's review what went on in this solution.
What the \pm±plus minus sign means
Note that every positive number has two square roots: a positive square root and a negative square root. For example, both 666 and -6−6minus, 6, when squared, equal 363636. Therefore, this equation has two solutions.
The \pm±plus minus is just an efficient way of representing this concept mathematically. For example, \pm 6±6plus minus, 6 means "either 666 or -6−6minus, 6".