## Why do we Rationalise the denominator in Surds?

The reason is that if we need to add or subtract fractions with radicals, it’s easier to compute if there are whole numbers in the denominator instead of irrational numbers.

## How do I rationalize the denominator?

So, in order to rationalize the denominator, we need to get rid of all radicals that are in the denominator.

1. Step 1: Multiply numerator and denominator by a radical that will get rid of the radical in the denominator.
2. Step 2: Make sure all radicals are simplified.
3. Step 3: Simplify the fraction if needed.

Why do we rationalize the denominator?

We rationalize the denominator to ensure that it becomes easier to perform any calculation on the rational number. When we rationalize the denominator in a fraction, then we are eliminating any radical expressions such as square roots and cube roots from the denominator.

What is a surd in math?

A surd is an expression that includes a square root, cube root or other root symbol. Surds are used to write irrational numbers precisely – because the decimals of irrational numbers do not terminate or recur, they cannot be written exactly in decimal form.

### What are the rules of Surds?

The rules of surds are:

• Rule 1: = √(r*s) = √r*√s.
• Rule 2: √(r/s) = √r/√s.
• Rule 3: r/√s = (r/√s) X (√s/√s)
• Rule 4: p√r ± q√r.
• Rule 5: r / (p+q√n)
• Rule 6: r / (p-q√n)

### How do you simplify Surds?

To simplify a surd, write the number under the root sign as the product of two factors, one of which is the largest perfect square. Note that the factor 16 is the largest perfect square. Recall that the numbers 1, 4, 9, 16, 25, 36, 49, are perfect squares.

What makes a number a surd?

What is the formula of Rationalisation?

To rationalize a +√b we need a rationalizing factor a -√b: (a +√b) × (a -√b) = (a)2 – (√b)2 = a2 – b. The rationalizing factor of 2√3 is √3: 2√3 × √3 = 2 × 3 = 6.

#### How to rationalise the fraction of a surd?

To rationalise the denominator, multiply the fraction by \\ (\\frac { {\\sqrt 3 }} { {\\sqrt 3 }}\\) Now try the question below. Sometimes the denominator might be more complicated and include other numbers as well as the surd. If this is the case you need to multiply the fraction by a number that will cancel out the surd.

#### How is the denominator of a surd simplified?

A fraction whose denominator is a surd can be simplified by making the denominator rational. This process is called rationalising the denominator. If the denominator has just one term that is a surd, the denominator can be rationalised by multiplying the numerator and denominator by that surd.

How to rationalise the denominator of a fraction?

Surds : How to Rationalise the Denominator easily. This video demonstrates how, by multiplying the numerator and denominator by the same surd, that we can rationalise the denominator of a fraction. This, effectively, moves the surd from the denominator to the numerator of the fraction thus making the denominator a rational number

When do you use a Surd in decimal form?

Surds are numbers left in square root form that are used when detailed accuracy is required in a calculation. They are numbers which, when written in decimal form, would go on forever. A fraction whose denominator is a surd can be simplified by making the denominator rational. This process is called rationalising the denominator.