72 is not a perfect square. It is represented as √72. The square root of 72 can only be simplified….Square Root of 72.

You can add or subtract square roots themselves only if the values under the radical sign are equal. Then simply add or subtract the coefficients (numbers in front of the radical sign) and keep the original number in the radical sign.

If different order surds have the same base then their product can easily be obtained using the laws of indices. Multiplication of surds can be obtained by simply following the law of indices. Like 2√3×2√3 = 3, so the product of two similar surds is rational number.

Adding and subtracting surds The rule for adding and subtracting surds is that the numbers inside the square roots must be the same. Example 5 2 − 3 2 = 2 2 This is just like collecting like terms in an expression . 4 2 + 3 3 cannot be added since the numbers inside the square roots, are not the same.

When we come to multiply two surds, we simply multiply the numbers outside the square root sign together, and similarly, multiply the numbers under the square root sign, and simplify the result. A similar procedure holds for division. The usual rules of algebra also, hold when pronumerals are replaced by surds.

Solution:

1. Express √2 as a surd of order 6. Solution: √2 = 21/2. = 21×32×3. = 236. = 81/6. = 6√8. So 6√8 is a surd of order 6.
2. Express ∛3 as a surd of order 9. Solution: ∛3 = 31/3. = 31×33×3. = 339. = 271/9. = 9√27. So 9√27 is a surd of order 9.
3. Simplify the surd ∜25 to a quadratic surd.

Solution. The order of the surd is 2.

Solution. 27 4 = 3 × 3 × 3 4 which is irrational. ∴ is a surds.

The order of the surds is 4.

Answer: 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.

The order of the surd is 3.

When we can’t simplify a number to remove a square root (or cube root etc) then it is a surd. Example: √4 (square root of 4) can be simplified (to 2), so it is not a surd!