- 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)

In mathematics, the law of surds generally implies the square root of a given number which cannot be further simplified to a whole number or a rational number. By nature, surds cannot be perfectly represented within a fraction.

In order to simplify a surd: Find a square number that is a factor of the number under the root. Rewrite the surd as a product of this square number and another number, then evaluate the root of the square number. Repeat if the number under the root still has square factors.

3 + 2 is not a surds because 3 + √2 is irrational.

So for example, √7 is a surd, and as it is irrational, its decimal expansion would go on forever without a recurring pattern. Note that square roots of decimals or fractions are not always surds. For example, √6.25=2.5 which is rational and therefore not a surd.

As 2 is a rational number, hence 4√16 is not a surd.

What Are the Rules of Surds?

- Surds cannot be added. √a+√b≠√(a+b)
- Surds cannot be subtracted. √a−√b≠√(a−b)
- Surds can be multiplied. √a×√b=√(a×b)
- Surds can be divided. √a√b=√ab.
- Surds can be written in exponential form. √a=a12n√a=a1n.

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.

The square root of 3 is represented as √3 or 3^{1}^{/}^{2}.

In Mathematics, surds are the values in square root that cannot be further simplified into whole numbers or integers. Surds are irrational numbers. The examples of surds are √2, √3, √5, etc., as these values cannot be further simplified.

The surds which have the indices of root 2 are called as second order surds or quadratic surds. For example√2, √3, √5, √7, √x are the surds of order 2.

- Step1 :Simplification of surds. 2 3 , 3 6 , 4 9 = 2 1 3 , 3 1 6 , 4 1 9. LCM of the denominators of the exponents. Multiplying the exponents with. 2 1 3 × 18 = 2 6 3 1 6 × 18 = 3 3 4 1 9 × 18 = 4 2. ...
- Step2 : Arrange in ascending order. 2 6 = 64 3 3 = 27 4 2 = 16. Ascending order. Hence, option A is correct. Suggest Corrections.

In Mathematics, the square root of 15 is a number that when multiplied by itself yields the original number 15. Because it cannot be stated in the form of p/q, the square root of 15 is an irrational number.

The square root of 20 is represented as √20, where √ is the radical sign and 20 is said to be radicand. In the simplest form, the √20 can be written as 2√5. Therefore, here we cannot say that √20 is a rational number since √5 is an irrational number.

The number underneath this radical symbol is known as radicand. Hence, the number whose square root is to be determined is called the radicand. In this case, 8 is the radicand and 2√2 is the simplest and the radical form of √8. This value is called surd since you cannot simplify this further.

37 =731. The order of surd is 3.

For example, √9 is a surd because it cannot be simplified to 3/3 or any other rational number.

The square root of 50, 7.0710678…, is an irrational number since it is a non-terminating decimal.

The square root of 12 is represented in the radical form as √12, which is equal to 2√3. Since 2√3 cannot be further simplified, hence such roots are called surds.

The square root of 52 is 7.211.

Square root of 125 is a not a natural or a whole number but an irrational number. 125 is an odd composite number. 125 is an imperfect square, hence no natural number can be squared to get the original number. 125 is a perfect cube, (125 = 5^{3}) hence the cube root of 125 is 5.