give me sums of quadratic surd with solutions.....please atleast 10 sums..
Answers
Answer:
We will look at simplifying quadratic surds, and at how to add, subtract, multiply ... each of the terms in the sum, because they all contain the same quadratic surd .
Suppose that the area of a square painting is 8 square inches, and we want to know the lengths of its sides to determine if it will fit in a particular place on our wall. The area of a square is equal to the square of its side length.
A = s2, where s is the length of the side of a square.
Therefore, to find the length of the side of our painting, we plug in 8 for the area (A), and solve the resulting equation for s.
Suppose that the area of a square painting is 8 square inches, and we want to know the lengths of its sides to determine if it will fit in a particular place on our wall. The area of a square is equal to the square of its side length.
A = s2, where s is the length of the side of a square.
Therefore, to find the length of the side of our painting, we plug in 8 for the area (A), and solve the resulting equation for s.
quadsurd1
We end up with s = √(8), or 2√(2), so this is the length of one side of the painting. Great! This will fit perfectly!
In mathematics, we call the number √(8) a quadratic surd. A quadratic surd is an expression containing square roots, such that the number under the square root is a rational number and is not a perfect square.
quadsurd2
Notice that when we solved for the side length of the painting, we got √(8), but the final answer was 2√(2). This is because we simplified √(8) to get this.
When it comes to quadratic surds, putting them in simplest terms means to rewrite them so that the number under the square root has no divisors that are perfect squares. To simplify a quadratic surd, we use the following steps:
Factor the number under the square root so that it is written as a product of perfect squares and a number that is not a perfect square.
Split up the expression into a product of square roots of each factor.
Simplify.
We can observe this process by simplifying √(8) in the image.
Step-by-step explanation:
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