Question

Can you get a pure surd when you find
(i) the sum of two surds
(ii) the difference of two surds
(iii) the product of two surds
(iv) the quotient of two surds
Justify each answer with an example

Answer 1

Answer:

Yes, we can find a Pure surd by adding two surds but the surds to be added must be same.

Step-by-step explanation:

For Example:

√a + √a=2 √a

The answer here is not in pure form but it can be converted into pure form as shown below.

2 √a= √(2.2) √a = √(2.2a)= √(4a) Because √(2.2) = 2

So we also come to know that a Mixed Surd can be converted into Pure Surd and vice versa.

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Answer 2

Answer:

i) the sum of two surds.

    $\sqrt2$ + $\sqrt2$ = $2\sqrt2$

Convert it into pure surd, then we get

     $2\sqrt2$  =  $\sqrt8$

$\sqrt8$ is pure surd. Hence the answer is yes.

ii) the difference between the two surds.

      $\sqrt10 - \sqrt5 = \sqrt5$

Convert into pure surd, then we get

      $\sqrt10- \sqrt5 = \sqrt5(\sqrt2 - 1)$

Yes, we get a pure surd.

(iii) the product of two surds

       $\sqrt10$×$\sqrt5 = \sqrt50$

Hence, the answer is yes.

(iv) the quotient of two surds

      $\sqrt(35/7) = \sqrt5$

Yes, we get a pure surd.

A surd is a phrase that contains a square root, cube root, or other root sign. Surds are used to precisely represent irrational numbers because their decimals do not finish or recur, hence they cannot be written exactly in decimal form.

The various sorts of surds are as follows:

• Simple Surds - A simple surd is one that has only one phrase. Example: $\sqrt2, \sqrt5$

• Pure Surds are fully unreasonable Surds. $\sqrt3$ as an example

• Surds with Similar Surds - Surds with the same common surds factor.

• Surds that are not fully irrational and may be expressed as a product of a rational number and an irrational number are known as mixed surds.

• Compound Surds - An expression formed by adding or subtracting two or more surds.

• Binomial Surds - A surd composed of two other surds.

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