Expanding And Simplifying Surds | Maths

In this video, you will learn how to expand and simplify surds. A surd is an irrational number that cannot be written as a simple fraction or a terminating decimal. Surds often involve square roots or cube roots of non-perfect squares or cubes.

To expand a surd, we use the distributive property of multiplication. For example, to expand (a + b)√c, we multiply a by √c and b by √c, and then add the two terms. So, (a + b)√c = a√c + b√c.

To simplify a surd, we need to simplify the radical to its simplest form. This means that we need to find the largest perfect square that is a factor of the number under the radical. Then, we can simplify the surd by taking the square root of the perfect square factor outside of the radical. For example, to simplify √50, we can factor 50 as 25 * 2. Then, we can simplify √50 as √25 * √2, which is 5√2.

To expand and simplify more complicated surds, we use a combination of these techniques. We can expand the surd using the distributive property, and then simplify the resulting expression by simplifying each term. We can also simplify the surd first, and then expand the simplified expression using the distributive property.

By following these steps, you can expand and simplify surds with confidence. Remember to factor the number under the radical to find perfect square factors, and use the distributive property to expand the surd. With a little practice, you'll be able to tackle even the most challenging surds.

Expanding the expression using FOIL (First, Outer, Inner, Last) method, we get:

(2 + √5)(1 - √5) = 2(1) + 2(-√5) + √5(1) + √5(-√5)
= 2 - 2√5 + √5 - 5
= -3 - √5

Therefore, (2 + √5)(1 - √5) simplifies to -3 - √5.

Happy Learning !!!

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