# Surd

Updated: 26 Aug 2023

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Among the vast fields of mathematics, surd hold a special place. Surds are irrational numbers in various mathematical expressions, equations, and real-world scenarios. This article is about the definition, properties, explanation, examples and MCQs about surds.

## Definition of Surd

The irrational root of a rational number is called a surd. A number of the form of \sqrt[n]{a} is called Surd, where a is a positive rational number.

*A number will be a surd, if*

- It is irrational
- It is a root
- A root of a rational number

## Examples of Surds

\sqrt{3} and \sqrt{5+\sqrt{3}}

- In the above examples, both are irrational numbers.
- The first number is a root of rational number 3 , whereas the second number is a root of irrational number 5+\sqrt{3} .
- Thus, \sqrt{3} is a surd and \sqrt{5+\sqrt{3}} is not a surd.
- \sqrt[3]{8} is not a surd because its value is 2 which is rational.
- \sqrt{-2} , \sqrt{-3} are not surds because -2 \ and \ -3 are negative.

## Conjugate of Surds

- The conjugate of a\sqrt{x}+b\sqrt{y} is a\sqrt{x}-b\sqrt{y} .
- Similarly the conjugate of 5+\sqrt{3} \ is \ 5-\sqrt{3}

## Surds MCQs

1. A number of the form of \sqrt[n]{a} is called ______, where a is a positive rational number.O Conjugate

O Surd

O Rational

O None of these

## Show Answer

**
Answer:
Surd
**

2. The rules for surd is/are _________

O It is irrational

O It is a root

O A root of a rational number.

O All of these

## Show Answer

**
Answer:
All of these
**

3. In a surd, \sqrt[n]{a}, n is called ______ of the surd.

O type

O order

O conjugate

O None of these

## Show Answer

**
Answer:
Order
**

4. \sqrt{3} is

O a surd

O not a surd

O conjugate of a surd

O None of these

## Show Answer

**
Answer: a surd
Explanation:
Here is the root of rational number, so it is a surd
**

5. \sqrt{5+\sqrt{3}} is

O a surd

O not a surd

O conjugate of a surd

O None of these

## Show Answer

**
Answer: not a surd
Explanation:
Here the root of irrational number, so it is not a surd.
**

6. \sqrt[3]{8} is

O a surd

O not a surd

O conjugate of a surd

O None of these

## Show Answer

**
Answer: not a surd
Explanation:
\sqrt[3]{8} is not a surd because its value is 2 which is rational.
**

7. \sqrt{3} is called _____ surd.

O Quadratic

O Cubic

O Biquadratic

O None of these

## Show Answer

**
Answer: Quadratic
Explanation:
Here the surd index order is 2, so it is called quadratic.
**

8. \sqrt[3]{3} is called _____ surd.

O Quadratic

O Cubic

O Biquadratic

O None of these

## Show Answer

**
Answer: Cubic
Explanation:
Here the surd index order is 3, so it is called cubic.
**

9. \sqrt[4]{3} is called _____ surd.

O Quadratic

O Cubic

O Biquadratic

O None of these

## Show Answer

**
Answer: Biquadratic
Explanation:
Here the surd index order is 4, so it is called biquadratic.
**

10. \sqrt[3]{3} \ and \ \sqrt[3]{5} is called _____ surds.

O Quadratic

O equiradical

O Biquadratic

O None of these

## Show Answer

**
Answer: equiradical
Explanation:
Surds of the same order are called equiradical surds which is 3.
**

11. \sqrt{3} is called _____ surd.

O Monomial

O Binomial

O Trinomial

O None of these

## Show Answer

**
Answer: Monomial
Explanation:
Surd consists of one term is called monomial.
**

12. \sqrt{3}-2 is called _____ surd.

O Monomial

O Binomial

O Trinomial

O None of these

## Show Answer

**
Answer: Binomial
Explanation:
Surd consists of Two terms is called binomial.
**

13. 2-\sqrt{3}+\sqrt{5} is called _____ surd.

O Monomial

O Binomial

O Trinomial

O None of these

## Show Answer

**
Answer: Trinomial
Explanation:
Surd consists of three terms is called trinomial.
**

14. Expressions containing two or more surds are called _____ surds.

O Monomial

O Binomial

O Compound

O None of these

## Show Answer

**
Answer:
Compound
**

15. \sqrt[3]{5} is called _____ surd.

O an entire

O mixed

O Trinomial

O None of these

## Show Answer

**
Answer: an entire
Explanation:
If the coefficient of the surd is \pm1 is called an entire surd.
**

16. -4 \sqrt[3]{5} is called _____ surd.

O an entire

O mixed

O Trinomial

O None of these

## Show Answer

**
Answer: mixed
Explanation:
If the coefficient of the surd is other than \pm1 is called mixed surd.
**

17. \sqrt{8} and \sqrt{18} are _____ surds.

O Similar

O Like

O Both a & b

O None of these

## Show Answer

**
Answer: Both a & b
Explanation:
\sqrt{8}=\sqrt{4 \times 2}
\sqrt{8}=2\sqrt{2}
AND
\sqrt{18}=\sqrt{9 \times 2}
\sqrt{18}=3\sqrt{2}
**

18. Conjugate of 3-\sqrt{5} is

O -3-\sqrt{5}

O -3+\sqrt{5}

O 3+\sqrt{5}

O \sqrt{3}+\sqrt{5}

## Show Answer

**
Answer: 3+\sqrt{5}
Explanation:
The conjugate of
a\sqrt{x}+b\sqrt{y} is
a\sqrt{x}-b\sqrt{y}
**

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